The broadcaster said Stoudemire was coming off the floor at American Airlines Arena following the Knicks' 104-94 first-round loss to the Miami Heat when he put his hand through the glass enclosing a fire extinguisher, apparently out of frustration.
The report said paramedics were called into the Knicks' locker room to treat Stoudemire, whose hand was badly lacerated.
The 6-foot-10, 250-pound front court player was shown leaving the arena with his arm in a sling, although no cast was visible.
The Knicks didn't immediately issue a report on Stoudemire's condition or availability for Game 3, set for Thursday in Madison Square Garden.
New York faces a 2-0 deficit in the Eastern Conference quarterfinal series after dropping an NBA record-tying 12th straight post-season contest.