Can I do a multi day cycle tour in Germany now (during Corona time), on my own, camping in public places?

You cannot even camp in public places to begin with, period — virus or not. Case closed. See https://outdoors.stackexchange.com/questions/10809/why-is-it-prohibited-to-sleep-in-a-tent and Is wild camping possible in Germany? Where?, for starters.

In short: No.

_{Although of course, for “can” in its literal meaning, it’s “yes”.}

First, hotels and the like are presently not allowed to accept you, as are camping sites, so you would necessarily have to do the equivalent of “wild camping”. Which is your initial premise, too, if I understood right.

Also, and more importantly, doing a tour across the country (moving through large areas, and across regions needlessly, having contact with many people in many different regions) is exactly the thing that the government presently doesn’t allow for. And seeing how traffic is greatly reduced to almost zero, you are likely (guaranteed?) to be noticed.

Even if bike tours across the country are not explicitly declared being illegal (neither is it explicitly illegal to, I dunno, spit at someone?), it’s pretty darn obvious that you will be willfully acting against the Kontaktverbot in a very explicit and significant way, so you will not be able to talk yourself out of that.
This may have some very noticeable consequences from monetary fees in the hundreds to low thousands (depending on where you’re caught) to possibly something more serious (not sure if “bodily harm” could be alleged, but might as well, especially in a few days from now, I wouldn’t risk it).

As for wild camping (neglecting the other aspect), while some people — campers — argue that wild camping is not explicitly forbidden in Germany, and therefore allowed, that is far from the truth. The same people argue that it is explicitly allowed for everybody to go to “free areas” for recreational purposes. While this is true, it is only the half truth, though. To begin, “go” (as in walk) does not imply “camp”, so that logic is flawed.

Further, it is explicitly forbidden to camp in many (in fact, most) places and under many conditions, nation-wide, state-wide, and regionally.

It is forbidden to camp in the forest (it is even explicitly forbidden to walk off the path after dusk, and sometimes even during the day) or in a variety of “bio areas” such as e.g. coasts, bioreserve, and bio-whatever-biotop-alikes, or near creeks (which, in summary, is almost everywhere, and it’s very hard to tell where you actually may be allowed to camp).
It is explictly forbidden to do a hundred other seemingly harmless things that one also does while camping (anything that could possibly disturb an animal) during “vegetation period” which is from March to September, which is… right now.
It is further explicitly forbidden to do “wild camping” in Niedersachsen, Sachsen, Sachsen-Anhalt, Thüringen and Saarland, at all times, and without exception.

So, you may in principle only camp in some states, in no-forest areas, far from the coast and far from creeks, outside settlements, and whatnot. And… only if despite being “free area” it’s not private property, which you cannot tell easily (camping on private property without the owner’s consent is forbidden nation-wide).

That doesn’t mean you couldn’t do it and possibly get away with it. But I wouldn’t deem it a very clever or risk-free endeavour right now.

Summary: longer bike tours come with a lot of contacts.

Almost all these can be avoided by doing short tours since you can take all your supplies with you for a day or two. This still leaves you 50 – 150 km x 360° from where you are in non-contact-mode.

Long version:

Being in “no contact, but go out and get some fresh air and sun on your own” Hesse the idea also briefly crossed my mind…

However, in addition to averell’s answer with which I wholeheartedly agree, consider:

• Camping is typically more lax on hygiene than everyday life. This may not be the best idea right now.

• Don’t underestimate how much contact one has on a bike tour compared to the semi-hermite lifestyle recommmended right now.

  • You’d probably go and buy groceries far more often than with a semi-hermite minimize-your-contacts-lifestyle: I can easily do now with once per week (or even less) to the supermarket/butcher/baker. On a bike, that’s called expedition, not tour 😉
  • You need to get water even more often. Every time you ask somewhere is a contact right now.

• If you want to wash your hands regularly, often and throroughly, you need even more water. Right now, pubs & co. are closed. I read in the news that truckdrivers complain they have a hard time finding toilets (gas stations may have decided to close theirs since in order to not expose the cleaning staff). And besides, these are places where lots of people pass.

• If you do contract Covid-19, you may spread it along your way. The idea behind the lockdown is to get the situation back to where public health has a chance to contain the spread because they can trace contacts. A stealth camping tour directly counteracts this.

• What is your plan for getting back in case you get sick? Hopefully not to take the train.

Of lesser concern:

• I live in a rual area and these days I actually see considerably more people in the fields than usual: People are making the best of the situation and enjoying the brilliant sunshine walking, hiking or biking.
  Keeping your distance is no problem, but stealth camping may not be as stealthy right now as you’d like it to be.

• Wrt. being caught*: my guess is that right now there’s a high risk that whoever finds you lacks their usual humor and may not be willing to overlook that you skipped some rules.

* I conclude from the question that OP is aware that stealth camping is not allowed – one needs to ask the owner of the land for permission, and then it’s fine – but that isn’t called stealth camping.

TL;DR: You can, possibly, in some places, but it may not be a great idea.

Whether it is legal depends on the Bundesland (state) — to put it simply, the federal government has no authority in these matters, and each state put down their own rules. There are federal rules for entry into Germany, but these don’t apply as you are already in the country.

Example rules

For example: In Saarland they implemented a lockdown (possibly due to their proximity to the heavy-hit regions of France): You may only leave your home due to “important reasons”. On the other hand Rheinland-Pfalz has a “contact prohibition”, which means that you can free to go wherever you want, as long as you are with no more than one other person.

Also, individual cities have the right to be more restrictive.

Things change

Case numbers will rise in Germany and regulations may become more strict at any moment. In which case it may be difficult for you to go back home (also: Do not count on any restrictions being lifted until well after Easter — at best)

Infrastructure is shut down

However, even in Rheinland-Pfalz accommodations are not open for touristic purposes. This will include campgrounds. “Wild” camping is only regulated by the Länder, but generally there will be restrictions, and camping spots may be cordoned off.

Also, most public services that are useful for travellers are also shut down.

Enforcement

It is difficult to say how things will be enforced. Generally there’s no formal requirements in Germany, unlike in Italy or France. They will still stop and fine you if you blatantly flout the rules. My guess is that nobody will go and check for wild camping in the middle of nowhere, but they may check popular camping spots to make sure people don’t congregate there.

Responsibility

Cycling alone is not really an (additional) risk, as long as you don’t meet people. However, the question is if it is going to be a fun trip if you

• can’t go in places like the Saarland,
• keep to yourself all the time,
• have to find a remote spot to pitch your tent each night, and have no access to sanitary facilities,
• have to bring/buy and cook your own food (there will be no restaurants).

Plus, Germany is a densely populated country — it will be hard to really be alone. And as soon as more than one person pitches their tent in one place, the police will likely see that as a “congregation” and break it up.

In all honesty, it is probably a better idea to stay put in one place. If the local laws allow it, you can still go cycling and return to your home each night.