I drunkenly told a professor something fundamentally wrong about a friend's thesis work. Should I clarify and/or apologize?

I don't see why Germany should be any different from other places, but generally it is a good idea to apologize for stupid things said drunkenly. And since this may have a bearing on the reputation of a third party you probably have an obligation to make sure the record is correct.

Sooner is better than later in such things, so the professor doesn't spend effort on a lost cause.

This shouldn't be a big deal. If I were in your position I would simply email the professor and apologise, say you had made a mistake. But keep it professional, don't make a big deal about it, and you don't need to draw attention to the fact you were drunk... especially since not everyone's drunkenness presents as making up random things about people, and it might lower the professor's opinion of you. Just say something along the lines of, "Hi, it was nice to have a chat the other night. I know I spoke to you about x, but I realise I was mistaken."

There is no need to apologise for being drunk, as this is really not relevant; such a mixup could happen in any state of mind. There is also no need to apologise profusely for giving him false information; it is just a small mixup that is of little consequence to anyone. To keep the consequences at a minimum, it would grace you to spare your professor the wasted time of looking up (or even going through) an irrelevant thesis, by sending him an email along the following lines:

Dear X,

A few days ago I suggested that my coworker's masters thesis might be of interest to you, as its topic is related to your field. Today I realised I got his thesis mixed up ; his is not at all related to your work. Sorry for the confusion.

Regards,

You could start off the email with some niceties depending on how familiar you are.