The injury to Martin's right wrist will sideline him indefinitely, the Timberwolves said.
A further evaluation over the next few days will determine whether he will need surgery, the team (3-7)said.
The injury occurred at 6:48 of the first quarter in Minnesota's 115-99 win over the visiting Knicks on Wednesday (local time), and Martin went on to register his season-high for points.
Through nine games this season Martin is averaging 20.4 points on 48.3 percent shooting from the floor and 48.1 percent from the three-point line as Minnesota's leading scorer.
He joins a number of injured Timberwolves that includes Nikola Pekovic, Ricky Rubio and Ronny Turiaf.