On Tuesday, Towns had an MRI on the wrist, which revealed the injury. He will be further evaluated over the All-Star break, according to the team.
Timberwolves coach Ryan Saunders said before Wednesday's game that he did not know when or how Towns was injured. Towns had 23 points, 10 rebounds and 7 assists in 37 minutes in Monday night's loss to Toronto.
"He's a guy who takes a lot of contact," Saunders said. "He's a guy who attacks the rim with force. There's been times where he's getting knocked to the floor. So we know that there is wear in that sense but no specific action."
Towns is averaging a career-best 26.5 points and 10.8 rebounds in 35 games this season. He missed 15 games earlier this season because of a sprained left knee.
The Wolves led for most of the first three quarters Wednesday but blew a double-digit lead to fall in D'Angelo Russell's home debut. Russell, whom Minnesota acquired last week from the Golden State Warriors, finished with 26 points and 11 assists.
Wednesday's game was the Timberwolves' last before the break. Their next game is Feb. 21 against Boston.
Information from The Associated Press was used in this report.