Ortiz also sat out Sunday's comeback victory in Texas.
"I talked to him on the plane after the game and then again when he showed up today," Francona said. "It could be me being overly protective, but I want to make sure he's OK for the long haul. We don't need him to steal bases, but I think when he gets in that crouch of his, that comfort zone hitting, and he comes out of it, he feels it. And I actually think he's been taking some great swings. But I don't want him to go through the year like that so we're going to be a little careful."
Francona was non-committal when asked if Ortiz would pay Tuesday night.
"I think it depends on how he feels," Francona said. "I think there's a good chance he could play but I think there's a chance he might not play. How's that? That's probably about as honest as I can get."
Ortiz believes that the tightness occurred from his recent bout with the flu, which caused dehydration.
"I got the flu before and it just whooped me," Ortiz said. "I've been having tightness in my hamstring and groin. It's just bothering me when I try to run and all that stuff. They're just trying to take it easy on me and take me slowly through it."
Big Papi came down with the flu on May 17, when the Red Sox played a day-night doubleheader against the Tigers. Ever since that, his legs haven't felt quite right.
"I had a bad flu," said Ortiz. "I'm better. It was those rainy days we had. That doesn't help you when you have a bad cold and things like that. I just got an IV the other day [in Texas]. The IV helps you because it's a little more direct to the system."
Ortiz wasn't sure if there's some correlation between the hamstring woes and the fact he's in the midst of his longest drought without a home run (15 games and 52 at-bats) during his entire stint with the Red Sox.
"When I run, I put pressure on it. And for hitting, I sit on my leg to hit," Ortiz said. "I wouldn't be able to swing hard like I normally do. When I swing hard, my hamstrings tighten up and hurt me. It's not good."
Beckett good to go: Right-hander Josh Beckett will be activated from the disabled list in time to pitch Tuesday night's game against the Indians. Beckett missed two starts because of an avulsion on his right middle finger.
Before the injury, Beckett was on fire, going 7-0 with a 2.66 ERA.
Don't expect Beckett to be on a low pitch count on Tuesday.
"We would try to somewhat use our head. I think we'd be crazy not to," Francona said. "But no, he's fine. We wouldn't have pitched him [if he wasn't]. ... He could have pitched last week. We did this so there wouldn't be restrictions. He can go out and be the pitcher he is. Now, if we get to a certain point in the game, we might cut him back an inning, we'll see."
To clear a spot for Beckett on the roster, reliever Manny Delcarmen was optioned back to Triple-A Pawtucket following Monday's 5-3 victory over the Indians. Delcarmen was recalled on May 21, but he pitched in just one game for Boston.
"He needs to pitch," said Francona. "He will go down and pitch an inning [Tuesday]. He's going to report right away so he can get an inning and get back on track."
Timlin still in holding pattern: After giving up two hits and two runs over just two-thirds of an inning at Pawtucket on Sunday, Mike Timlin will make at least two more rehab appearances before being activated.
"He's going to go back to Pawtucket [on Monday] night and Thursday for another inning," Francona said. "The good news is he felt pretty strong and healthy. He didn't locate like he wants to or probably needs to. And again, he's frustrated. Not so much about going back but just that he didn't get through the inning last night. He had gotten to a pitch limit."
The Red Sox had given Pawtucket manager Ron Johnson a pitch limit of 20 for Timlin. He had reached 18 before being removed with two outs.
"He was frustrated because he wanted to finish the inning," Francona said. "We said, 'Put yourself in RJ's shoes. If you have a 10-pitch at-bat, somebody is calling RJ.' RJ did the safe thing. I don't blame him, I would have done the same thing."
Coco running them down: It is not your imagination. Coco Crisp has become a better center fielder this season than he was last. It seems that Crisp has been a near nightly presence on the defensive highlight film.
"I think he's playing center field with a lot of confidence," said Francona. "We talk about that at the plate, but he's playing defense with confidence. He's on the move. You look up and he's on the move. He's doing a great job out there. He's not just out-running balls. He's positioning himself. He's very aware. You see him move when certain hitters get to two strikes. He's done a great job."
Interestingly, the thing that Crisp seems to be most pleased with is the improvement he's made with his arm.
Crisp credits the improvement with a new arm slot that he's worked on with bench coach Brad Mills.
"When I used to throw as a second baseman, they had me throw from short," said Crisp. "In the outfield, I couldn't find my arm slot. Millsy told me to go back to the way I was throwing as a kid. It's weird, because I'm throwing from a shorter arm slot."
On deck: Beckett will be opposed by right-hander Jeremy Sowers (1-4, 6.29 ERA) in the middle game of this series on Tuesday. First pitch is scheduled for 7:05 p.m. ET.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.