The injury means Hunter, the team's projected No. 4 starter who has thrown just five innings in spring training games, is unlikely to be ready to start the season in the rotation.
"We now have one more spot come the first time or two through the rotation," assistant general manager Thad Levine said.
That means it's possible the Rangers could have two left-handed starters in the rotation when the season begins. Matt Harrison and C.J. Wilson have pitched well this spring in an effort to earn a starting spot.
"If they are the best we have, I'm certainly not against the idea," manager Ron Washington said. "I think Harrison showed you last night how far he's come since the last time he's competed. I don't think anybody can ignore what C.J. has been doing."
Harrison allowed two runs on three hits, but he had eight strikeouts and just one walk in his four innings of work in Thursday's 6-4 win over Milwaukee. Wilson is coming off a solid start and has given up four runs on six hits with eight strikeouts and one walk in nine innings of spring work.
Hunter was scratched from his start Thursday after experiencing pain while throwing changeups during warmups for his outing against the Milwaukee Brewers.
The Rangers said they would know more in the next few days, but Hunter would have to build up his arm strength once he returns to baseball activities and likely won't be fully ready by Opening Day.
Hunter, 24, was a member of the Rangers' rotation for the final three months of 2009, posting a 9-6 record and a 4.10 ERA in 19 starts (112 innings). He had 64 strikeouts and 33 walks.
"You don't want to downplay it, but now, because the Texas Rangers have pitching, we don't lose much," Washington said. "Our main concern is that Tommy gets well. We'll have someone pick up what we expected him to do."