Stoudemire, who was his team's second highest scorer with 18 points and seven rebounds, left the American Airlines Arena with his left arm in a sling and his hand heavily wrapped.
Several media reports cited sources saying Stoudemire had hit the glass casing surrounding a fire extinguisher, although the team gave no details of how the injury occurred.
A fire extinguisher in the corridor between the court and the Knicks locker-room had the glass casing shattered and had to be replaced.
"I am so mad at myself right now, I want to apologize to the fans and my team, not proud of my actions, headed home for a new start," Stoudemire wrote on his Twitter account.
A Knicks team spokesman said the player had suffered a "laceration" and confirmed the injury happened after the game.
Knicks head coach Mike Woodson declined to discuss the situation when asked by reporters.
Game three of the Eastern Conference first-round series, which the Heat lead 2-0, takes place on Thursday in New York and Stoudemire's absence would be a major blow for a team already without injured Jeremy Lin and Imar Schumpert.
"We just know he has a laceration and he's probably going to be out," said Knicks center Tyson Chandler.
"It makes it tougher. Your emotions run high. In a split second, a decision can alter things. You can't fault anybody, we have got to deal with the repercussions," he added.