The speedy center fielder had an MRI exam earlier in the day, but the Yankees were waiting to try and determine whether it would be best to put him on the 15-day disabled list.
Damon, entering his 13th major league season, has never been on the DL. He was in the trainer's room receiving treatment before the game and issued a statement through a team spokesman.
"I'm feeling better today than I was yesterday. I'm going to get after it with the trainers for the rest of the day and see where we are tomorrow," Damon said. "I still have sexy calves."
Damon was hurt in Monday's victory over Tampa Bay.
"We'll see how it progresses," manager Joe Torre said. "He's obviously going to be our best barometer for this thing."
After New York's 7-6 loss to the Devil Rays, Damon said he wanted to test his leg by Saturday. If he's not available to play at all this weekend, going on the disabled list would probably be the best thing for the team, he said.
"The most I would miss if I did go on the DL would be 10 games," Damon said. "Hopefully, we'll keep seeing improvement. My body has always been a quick healer."
Melky Cabrera started in center field for New York and second baseman Robinson Cano was in the leadoff spot. If Damon is out for a while, Torre said Cabrera would be a more logical choice to bat leadoff once he starts swinging the bat better.
Damon's legs are a big part of his game.
"He's been around long enough to know there's certain things he can go on with," Torre said. "If this was September, I'd be a little more concerned that he would try to push it to the end."
Cabrera will fill in for Damon until he returns. If Damon has to go on the disabled list, the Yankees probably would call up an outfielder from the minors. New York repeatedly has said Bernie Williams is not an option.
Torre reiterated that the team is fortunate to have Cabrera as a replacement. He got plenty of playing time as a rookie last season because of injuries to fellow outfielders Hideki Matsui and Gary Sheffield. Cabrera batted .280 with seven homers, 50 RBIs and 26 doubles in 460 at-bats. He also scored 75 runs and stole 12 bases while playing excellent defense, especially in left field.
"This kid can play center field with anybody," Torre said.