Even though Mindestlohn does not apply to interns, who stay up to 3 months, it is still a bad thing for startups.
> http://www.gesetze-im-internet.de/milog/__22.html
The main exception is if the internship is required for finishing or beginning a degree course or done while a degree course (but read the text of the law yourself for the remaining exceptions).
This was criticized a lot when the law adopted, since there can be good reasons to do an internship even after finishing university even if it is paid really badly (say, as a reference).