Richards, 20, earned his first Bundesliga start for Bayern in the 4-3 win against Hertha Berlin on Oct. 4 -- becoming the first American to start a Bundesliga match for Bayern in the 120-year history of the club -- and has gone on to make seven appearances in all competitions this season.
He made his debut for Gregg Berhalter's USMNT outfit in November's 6-2 victory against Panama, after recovering from a minor calf injury following his Bayern bow.
Hoffenheim are 12th and lost 4-1 to Bayern on Saturday. Richards was on the bench but did not come on.
The move will allow Richards to play under former Bayern reserve team boss Sebastian Hoeness again, who is now in charge of Hoffenheim.