Martin suffered the injury early in the first quarter of Tuesday's NBA match but was able to play on and excel, scoring 37 points in the Timberwolves' 115-99 win.
The 31-year-old was caught when getting his first three points of the match on the board, but it was not until after the game that the severity of his injury became clear.
Martin was taken to hospital following the match, and a statement from the team on Friday confirmed he will be a long-term absentee.
"An MRI taken at Mayo Clinic Square on Kevin Martin's right wrist has revealed a fracture," it read.
"He will be sidelined indefinitely.
"Further evaluation will be done over the next few days to determine the next course of action."
It remains unclear whether Martin will require surgery to correct the fracture, but his loss comes a huge blow for the Timberwolves, with Ricky Rubio and Nikola Pekovic also on the sidelines.
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