Anthony first aggravated the knee in the first half of Monday's win against the Cleveland Cavaliers and hasn't been on the floor since.
Woodson said Anthony's status remains day to day. The team said Sunday he is questionable to play Monday against the Warriors.
The coach said Anthony reported earlier Saturday that his knee is "so-so" after receiving treatment during the team's morning shootaround.
Anthony's isn't the only health issue the Knicks have. The team announced on Saturday that forward Amar'e Stoudemire is scheduled to have a right knee debridement next week and will miss approximately six weeks.
As for Anthony, an MRI taken recently revealed no structural damage, he said. But there has been a fluid buildup in the back of it.
Woodson intimated that the team has no plans to drain the fluid in Anthony's knee at this point. The Knicks will continue with treatment and will give him time to rest. The team hasn't taken any further tests on the knee.
"I know he's getting his treatment and you don't always have to drain, you can treat and the swelling can go away that way as well," Woodson said. "We've just got to give it time and see what happens."
When Anthony does return, Woodson hopes to reduce his minutes.
Anthony has played an average of 37.8 minutes per game. He averaged 41 minutes per game in January and 38.8 in February. Woodson would like to play him closer to 35 minutes, his per-game average in November.
After Saturday night, the Knicks will embark on a season-long five-game, seven-day road trip against Western Conference teams.
Ian Begley is a regular contributor for ESPNNewYork.com.