Stoudemire, who had been playing well off the bench, will have the procedure to remove tissue within the week, the Knicks said Saturday before their game against the Jazz.
Stoudemire missed the first 30 games after having the same surgery, called a debridement, on his left knee during the preseason. He returned on New Year's Day and has averaged 14.2 points in 29 games as a reserve.
"I feel for the young man because he put so much time and hard work in, but we've got to go on," Knicks coach Mike Woodson said.
The Knicks were also without Carmelo Anthony, sitting out his third straight game with a sore and stiff right knee.
But the Stoudemire news was a surprise, since there was no indication there had been any problem with his surgically repaired knees until Saturday morning.
Stoudemire didn't take part in the Knicks' morning shootaround, and had an MRI later in the day.
Leading the Brooklyn Nets by 2 1/2 games entering play Saturday, the Knicks have to hope Stoudemire can return for the playoffs.
"It's a loss, a major loss, to what we're trying to do, but you know we're going to have to wait on him and continue our climb," Woodson said. "We can't sit and sulk and feel sad and upset about it. It's what it is and guys have got to step up and play."
Stoudemire has a history of knee injuries that made the $100 million contract he signed in 2010 uninsurable. The Knicks were being especially careful since his latest surgery, keeping him on a minutes restriction that started in the low 20s and had recently grown to 30 minutes a night.
And once Anthony was hurt, the Knicks had no choice but to use Stoudemire right to - and even over - that limit. He played 32 minutes Monday in Cleveland, the game in which Anthony was injured, and went 31 minutes two nights later in a victory over Detroit, tying his season high with 22 points in each game.
He scored 16 points Thursday in a loss to Oklahoma City, playing 29 minutes and even throwing down an impressive dunk over Thunder defensive star Serge Ibaka. So even the Knicks were surprised to learn they would be without him again.
"Not what we expected to hear, that's for sure," forward Steve Novak said. "It was like he was out there getting buckets, dunking on guys a day ago, and he's hurt, so I feel bad for him. I think that the way he was playing, his confidence was high, and you just don't want to see him get hurt again."
Though his main injury last season was his back, Stoudemire has battled knee injuries throughout his career. The Knicks originally said he would be out two to three weeks with a ruptured cyst in his left knee during the preseason, but that became a lengthy absence for surgery.
The Knicks already lost another reserve forward, Rasheed Wallace, likely for the remainder of the regular season because of foot surgery. Marcus Camby has been injury-prone, so Stoudemire's injury could open additional time for Kenyon Martin, who just signed with the Knicks last month after sitting out all season.
They are calling Anthony day to day. He received more treatment Saturday and it is unclear if he will play on their upcoming road trip, which includes what would be his first trip back to Denver since the Nuggets traded him to the Knicks in February 2011.