Stoudemire injured the hand while punching the glass case surrounding a fire extinguisher in a fit of anger following the Knicks' Game 2 loss to the Miami Heat Monday at American Airlines Arena.
A small muscle in his hand was surgically repaired in the procedure, the team said.
The Knicks said Stoudemire is doubtful for Game 4. The New York Post reported he isn't expected back for the entire series, which New York trails 2-0.
The player said via Twitter he was "not proud of my actions" and that "we have all done [things] out of anger that we regret."
Game 3 of the best-of-seven series is Thursday at Madison Square Garden.