Chandler felt pain after playing just under 39 minutes in the Knicks' win over Oklahoma City on Sunday. New York carries a 12-game winning streak into Tuesday's game.
"We're going to rest him tonight and then see how he feels tomorrow," Woodson said. "He'll let us know if he's ready to go for the Chicago game (on Thursday)."
Chandler's neck is a concern for the Knicks as they prepare for the postseason.
The All-Star center missed 10 games earlier this month because of a bulging disk in his neck.
He returned to the floor last week but complained of soreness in his neck after games against the Heat and Hawks.
Chandler seemed to improve in last Friday's win over the Bucks. He played 37 minutes against Milwaukee and said afterward that his neck felt "much, much better."
But Woodson said Chandler requested to sit out after feeling discomfort following Sunday's win in Oklahoma City.
"That was a physical game the other night," Woodson said. "He's sore so if he tells me he needs some rest, than I've got to listen and rest him and get him ready for the next game if he's capable of playing."
Woodson said if Tuesday's game were a playoff game, Chandler would be in uniform.
Kenyon Martin will start at center for the Knicks on Tuesday. The 35-year-old had missed the past two games due to a sore left knee.
Martin will be on a restriction of 25 minutes. He complained of soreness last week after playing no fewer than 20 minutes in 11 consecutive games. Martin did not play for the first four months of the season, signing with the Knicks in late February. He said last week that the recent increase in playing time caused soreness in his knees.
"We'll probably hold him somewhere close to 20 minutes and we'll go from there," Woodson said.
The Knicks can clinch the Atlantic Division title -- their first since 1994 -- with a win on Tuesday or a Brooklyn loss. They are also 2½ games ahead of Indiana in the race for the No. 2 seed in the Eastern Conference. A second-place finish in conference guarantees the Knicks home-court advantage through two rounds of the playoffs.
"We're still trying to accomplish those two things," Woodson said. "I feel good about the guys in uniform; they've just got to play."
Joining Chandler on the injury list is Marcus Camby, who is out for the third straight game with a left plantar fascia injury.
Woodson was asked if he'd consider resting Chandler and Martin for the remainder of the regular season with the Knicks on the verge of clinching the division crown.
He said the decision to rest would be up to his players.
"Tyson came to me, said he wanted to rest, so we're going to let him rest. And if Melo comes to me and says he wants to rest, we'll let him rest. It's just that simple," the coach said.