There is no timetable at this point for Martin's return but the veteran forward expects to be out through the All-Star break.
The Knicks return from the break on Feb. 18 on the road against the Memphis Grizzlies.
"Right now he doesn't have [a] comfort zone," Knicks coach Mike Woodson said. " ... He's having to experience some pain and he can't play so you've just got to be patient and try to seek the best medical attention for him and try to get him back when we can."
Martin, 36, is in a walking boot and may seek a second medical opinion. He first aggravated the ankle injury on Jan. 28 against Boston. Prior to that, he'd missed 10 days due to a left ankle sprain and tendinitis.
Martin admitted on Monday that he probably tried to come back to soon from his most recent injury.
"Sometimes you've got to listen to your body and not your heart," he said.
Martin, a 13-year veteran, has dealt with injuries to his left ankle for several months. He entered the season on a minutes restriction due to lingering soreness in the ankle. He originally hurt his ankle last April.
Martin said "overuse" contributed to the most recent discomfort. He has missed eight of the Knicks' last ten games.
"You're supposed to play through some stuff but just playing in pain ain't cool all the time," Martin said. "Not knowing about the next day, whether I'm going to be able to help the team or not [hurts]. So it's more frustrating than anything."
With Martin out, Amar'e Stoudemire will likely see an increase in minutes. Stoudemire hinted on Tuesday that he was frustrated with his playing time of late. He'd played a combined 21 minutes in two games since returning from an ankle sprain. The Knicks were cautious early in the season with Stoudemire's minutes due to his history of knee injuries.
Before Monday's game, Woodson said he and Stoudemire were "in a good place."
"We'll get him more minutes and see where he is. Hopefully the minutes will be beneficial and he'll feel good about himself the next day and be ready to go the next game," Woodson said. "That's kind of where we've been pretty much all season with Amar'e. It's been up and down in that area based on some of the injuries that he has had. We'll see where he is tonight."