Josh Harrellson replaced Stoudemire in the starting lineup. The rookie scored 14 points and grabbed 12 rebounds in a 114-92 victory.
Stoudemire originally suffered the injury during the Knicks' 99-82 loss Thursday to the Los Angeles Lakers.
Stoudemire said he suffered the injury while coming off of a pick-and-roll play.
"I rolled down the lane, I forget who it was, but he put a shoulder into me. He hit me on the roll and I twisted my ankle," he said.
Stoudemire's absence severely compromises a team already dealing with other injuries.
Guard Iman Shumpert and forward Jared Jeffries, two of the Knicks' top reserves, are out -- Shumpert is sidelined two to four weeks with a sprained right MCL, and Jeffries is sidelined one to two weeks with a right calf strain.
After beating the Boston Celtics on Christmas Day to open their season, the Knicks lost two straight road games before Saturday's victory.
ESPNNewYork.com's Ian Begley contributed to this report.