The team said that Stoudemire will undergo nonsurgical treatment for the back injury and will treat it with rehabilitation. But coach Mike Woodson did not rule out the possibility that Stoudemire could need surgery in the future.
After Monday night, the Knicks will have just 16 games left in the regular season, giving Stoudemire little time to recover if he undergoes surgery.
"You don't wish it on any player, especially Amare," Woodson said of the back injury.
Stoudemire is seeking a second opinion in Miami.
"Hopefully the second opinion is something. Since he was out all [last] summer rehabbing it and getting treatment on it, I'm hoping it's nothing too serious at this point," teammate Carmelo Anthony said. "My prayers go out to him and hopefully we can get him back as soon as possible."
Woodson said that Steve Novak and Josh Harrellson will have an increased role with Stoudemire out. Reserve forward Jared Jeffries would also be a candidate for a bigger role, but he is out for at least two weeks with a sore right knee.
"We can't look back," Woodson said of the Knicks, who entered play at 24-25 and 1½ games ahead of Milwaukee for the eighth and final playoff spot in the Eastern Conference. "We've got to continue to play and try to win games."
Both Stoudemire and Lin originally suffered injuries in the second half of Saturday's 101-79 win over the Detroit Pistons.
"Just thinking that more rest would be beneficial right now and that's basically it," Lin said as to why he's sitting. "Just trying to make sure that we give me a chance to rest so that I don't force anything before I have to."
Lin did not rule out the possibility of returning Wednesday against the Magic.
"I just want to make sure when I come back that I'm 100 percent," Lin said.
Stoudemire has had back issues in the past.
The 29-year-old pulled a muscle in his back during the 2011 playoffs. He needed most of the NBA's five-month lockout to rehab the injury, playing in a five-on-five game just once during the lockout. He struggled early in the shortened 66-game season, but Stoudemire appeared to be getting his rhythm back recently, averaging 18 points per game on 57 percent shooting in his last five games.
"He's got to keep his head up," Woodson said. "If he has to have surgery, he's gotta rehab and come back. He's still a young player."
Chandler said that while Stoudemire's absence will be felt, he's confident the bench will compensate for the loss.
"We all gotta step up," he said. "I've been saying all year that our team is very deep, so it's an opportunity for somebody to step up and he has to take advantage of it."
That somebody is likely rookie big man Harrellson, who played extra minutes Saturday night in place of Jeffries. He finished with four points and seven rebounds against the Pistons.
Since recovering from a fractured right wrist, suffered Jan. 21 against the Denver Nuggets, Harrellson said it's improving every day -- he just can't move it all the way back just yet -- and he's getting his wind back to give the energy Stoudemire has been providing lately.
"Just go out there and hustle. Just try to do what STAT's [Stoudemire's nickname] been doing," Harrellson said. "He's been playing great defense, he's been running up and down the floor, he's been a tremendous basketball [player] these last couple weeks. He's definitely getting his legs back from sitting out all summer, so hopefully I can go in there and do the same thing. I sat out eight weeks and I'm trying to get my legs back right now, too. Hopefully I can just go out there and fill the shoes that he's been playing in."
On a positive note, Chandler has recently not been wearing a brace on his injured left wrist, including on Monday during shootaround, in order to get his motion back.
"It's a feeling a lot better," he said.
Ian Begley is a regular contributor to ESPNNewYork.com. ESPNNewYork.com's Jared Zwerling and Christopher Hunt was used in this report.