Davis suffered the injury Wednesday after appearing to step on another player's foot. He left the game and did not return to the Madison Square Garden floor, the Orlando Sentinel reported Thursday.
The Magic fell to the Knicks, 113-97.
The injury leaves a rebuilding team with a 14-31 record without its most effective low-post defender, the newspaper noted, adding Davis missed 11 games earlier in the season after he dislocated his left shoulder Dec. 19.
The Magic are 2-18 since Davis' shoulder injury.