"I think he's going to be out,'' Woodson said Thursday. "That's my gut."
Stoudemire was on the floor during practice but hasn't started running yet. The veteran power forward underwent surgery March 11 to clean up debris in his right knee.
At the time of the surgery, the Knicks said Stoudemire was expected to miss four to six weeks. Based on that timetable, the earliest he could return would have been April 22, a day before Game 2 of the first-round series.
On Thursday evening, Stoudemire stopped short of ruling himself out of the Knicks-Celtics series but did not put a specific timetable on his return.
"I'm doing everything I can to get back out there and be extremely strong and healthy so, hopefully, I'll be out there soon," Stoudemire said on Thursday at the premier of his documentary, "Amar'e Stoudemire: In The Moment," which will debut on EPIX on Friday.
The Knicks have thrived even with Stoudemire out, finishing the regular season 17-6 in their last 23 games and winning the Atlantic Division title for the first time in 19 years.
Stoudemire has dealt with injuries in each of his three postseasons with the Knicks.
In the Knicks' first-round series against Boston in 2011, Stoudemire suffered a back injury prior to Game 2 while attempting a dunk during warm-ups. He played through the injury, but averaged just 10 points in the final three games of the series.
Last season, he suffered a hand laceration after punching the glass casing of a fire extinguisher following a Game 2 loss to the Heat. He missed Game 3 of the series.
Stoudemire missed the first two months of this season while recovering from arthroscopic surgery on his left knee. In 29 games this season, the 10-year veteran averaged 14.2 points and five rebounds in 23.5 minutes, shooting 57 percent from the field.
In positive injury news for the Knicks, All-Star center Tyson Chandler said he's feeling 100 percent healthy.
Chandler had missed 16 of the Knicks' final 20 games with a bulging disk in his neck. He practiced with the team Thursday.
"It's the best I've felt in a long time," Chandler said. "It actually was a blessing in disguise that I was able to get that time off because now I'll have fresh legs throughout the playoffs and I'm excited for this long run we're about to endure."
Knicks starting guard Pablo Prigioni is questionable for Saturday's Game 1 because of a sprained right ankle. If Prigioni can't play, Woodson may opt to insert rookie forward Chris Copeland into the starting lineup and shift Iman Shumpert to shooting guard.
Ian Begley is a regular contributor to ESPNNewYork.com.