score:8
No this is not a problem. When you leave you will hand in the form that is presently stapled into your passport and you will be stamped out. When you return you will get a new 90 day period (in my experience).
It is possible that the immigration inspector will notice that you have been in Japan very recently. She/he may ask you about it. Of course you should be honest. However, since you intend to leave before your original 90 day period is up, you cannot be accused of trying to extend your period with a visa run. You may want to have a copy of your itinerary handy to show this.
Informally, I do not think Japan is worried about westerners coming to visit and making frequent entries, as long as they do not break the rules. I have always found the immigration staff to be very polite, courteous and friendly.
Upvote:1
Observation: US passport, we had an overnight connection in Tokyo. On the return flight we also had an overnight connection. This second entry didn't cause any scrutiny from the official and unless his computer found our tickets he didn't know it was just an overnight connection. (This actually made economic sense--it was part of an airline promo deal, they were putting us up at a hotel near the airport. The tickets were no more than the direct flight would have been, we got to spend some hours looking around at basically zero cost.)