Prince was booked into the Turner Guilford Knight Correctional Center on Thursday night, according to inmate records.
It wasn't immediately clear what charge Prince is facing.
In a statement, the Timberwolves said they are aware of the situation and are gathering more information.
The team signed Prince to a two-year, $16 million contract extension in June.
This past season, he established himself as a solid rotational player on a Timberwolves team that returned to the Western Conference playoffs, averaging 7.3 points and 2.5 rebounds a game in 17 minutes.