Baldelli saw the team doctor Wednesday and is scheduled to have an MRI in St. Petersburg on Thursday.
"Hamstrings are one of those type of injuries it's difficult to put a finger on right away," said Andrew Friedman, executive vice president of baseball operations. "The good news is it's higher up in his leg, which is better than it being lower in his leg."
Baldelli's hamstring problem in the spring was with his right hamstring and he missed about 10 days.
"We're going to be very smart and cautious with it," Friedman said. "We're fortunate to have the depth we have to step in. We want to insure his long term health."
Even without Baldelli, the Rays have Carl Crawford, Jonny Gomes, B.J. Upton, Delmon Young, Elijah Dukes and even Brendan Harris who can play the outfield.
Friedman said he's guessing Baldelli will be placed on the disabled list. If he indeed goes on the DL, infielder Greg Norton is the likely candidate to be called up. Norton has been on the DL since April 1, when he had surgery on his right knee.
While Baldelli is away, Dukes will get a lot of starts at the position and Upton will be used there as well.
Revised batting order: The Rays' batting order had a little different look on Wednesday night, with Dukes hitting in the leadoff spot, Upton batting second and Harris hitting sixth.
Rays manager Joe Maddon explained that Dukes does a nice job of drawing walks and that Upton can use the protection offered by Carl Crawford hitting in the No. 3 spot. Harris, who had four hits Tuesday night and entered Wednesday night's game with a .340 average, moved up to give some protection to Carlos Pena, who hit in the fifth spot.
"You look at the combination of speed and power of those first three guys, it's pretty good," Maddon said. "We'll see how it works out. Nothing right now is etched in stone."
Better in center field: Dukes has started 28 games this season, 18 in center field, one in left, and nine at DH. He is hitting .246 when he plays center field and just .195 as a DH.
Maddon said learning how to handle being the DH can be a tough obstacle for a young player.
"It's hard," Maddon said. "That's an easy leap people make -- 'Just DH him and we'll get him in the lineup.' And it's just not that easy. This guy's used to playing an entire game where he's focused on playing offense and defense. He loves playing defense also. This is a different routine. And he has tried everything. It's not easy to do that.
"We have to keep trying. We've just got to wait it out. He's gaining experience to do that also. ... I've been around [a lot of young players] in situations where you have three or four outfielders, and you put one [at DH] every once in awhile, it's not easy."
Maddon said players don't want to be the DH, and he can't blame them.
"They want to be complete baseball players," Maddon said. "And [Dukes] is one of those."
Turning the corner: The Rays seem to be closing in on being considered a respectable team. Left-hander Scott Kazmir believes the only thing keeping the team from turning the corner in that direction is more experience as a team.
"That's all it is," Kazmir said. "To be honest with you, we haven't played that good of baseball, all around. I don't think. And just our talent really got us the wins we have right now. ... It's just once we get more experience it's going to pay off. That's all it is."
Up next: The Rays and Rangers will wrap up their three-game series at Disney's Wide World of Sports on Thursday night with a 7:10 p.m. ET contest. Scott Kazmir will start for the Rays and will be opposed by right-hander Kameron Loe.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.