He suffered the injury Monday against the Minnesota Twins while running on a fielder's choice grounder in the sixth inning, and was not in the lineup for Thursday's game against the Twins.
He plans to discuss the situation with Manager Joe Torre before making a firm decision Saturday.
"I think we have to be smart," he said on the team's Web site. "The one thing you don't want to do is to keep going out there and get it worse, go into the break and do something that's not going to be helpful for the team."
For the season, Rodriguez is averaging .314 with 28 home runs and 80 RBI in 306 at-bats.
He was the American League's leading vote-getter for the All-Star Game next Tuesday at San Francisco.