The 24-year-old center will be further evaluated during the upcoming All-Star break.
It's unclear when Towns suffered his wrist injury. He played nearly 37 minutes against the Toronto Raptors on Monday, including the majority of the fourth quarter.
In his fifth season in the league, Towns has averaged 26.5 points, 10.8 rebounds, 4.4 assists, and 1.2 blocks per game this year.
Despite being selected as an All-Star in the previous two seasons, Towns is not billed as a participant in any All-Star Weekend activities at this year's event in Chicago. The timing of his current injury likely precludes his chances of being a last-second replacement.