Upvote:3
The Germany Trains (bahn.de) are offering this service but only in conjunction with a train ticket. You could probably buy dummy ticket: cheapest for Stuttgart to Munich would be around 13 Euros if you book in advance by a week or so. See https://www.bahn.de/angebot/zusatzticket/gepaeck (sorry, it's in German only)
There are also private carriers that offer this. DHL seems to be the cheapest and they are ubiquitous in Germany. They used to have a special offer for this, but this may have expired at the beginning of the year. https://www.dhl.de/en/privatkunden/pakete-versenden/deutschlandweit-versenden/reisegepaeck.html
Other options would be UPS or Hermes (which the Bahn uses) and a few more. To get a quote, you need to poke in your exact details (dimensions, postal codes, weight).
I would probably choose a carrier that has drop off and pick up points, close to your hotels. That makes dropping and retrieving the bag easier and the pick point can hold it for a day or two, depending on how long you are staying in Berlin.