A statement from the Knicks said Noah, who is serving a 20-game ban over a failed drug test, suffered a rotator cuff injury in his right shoulder in January.
The French star had attempted to shrug off the injury but a follow-up scan taken this month showed no sign of improvement, the Knicks said.
"Team doctors have recommended off-season surgery," the Knicks said. "No decision has been made yet regarding the surgery and a timeline for his return to the basketball court has not been determined."
A report on The Vertical website said Noah could face up to six months of rehabilitation from surgery.
Noah's injury caps a miserable first season in New York for the 32-year-old, who underwent arthroscopic knee surgery in February and has not played since.
In March he tested positive for a substance similar to steroids which was included in an over-the-counter supplement.
He was hit with a 20-game ban for the offence of which he has already served eight games.
In 46 games this season for the Knicks, all of them as a starter, Noah averaged 5.0 points, 8.8 rebounds and 2.2 assists.
The two-time NBA All-Star, who was named the league's 2014 Defensive Player of the Year, had also been nagged by a hamstring injury earlier this season.
Noah, the son of French tennis great Yannick Noah, holds US, French and Swedish citizenship and first made his mark as a collegiate star at Florida, leading the Gators to consecutive US national tournament titles in 2006 and 2007.
After being selected ninth overall by the Chicago Bulls in the 2007 NBA Draft, Noah played for Chicago until last July, when he signed a four-year deal worth $72 million with the Knicks.