"Seems to be [he'll be out] the minimum amount of time, but that doesn't help us right now," Rays manager Joe Maddon said.
Reyes is 1-1 with a 4.09 ERA and 17 saves in 34 appearances. But he didn't look like himself Monday night in Cleveland when he pitched two-thirds of an inning and allowed four earned runs on a grand slam by Grady Sizemore.
"He just felt it the other day," Maddon said. "Playing catch yesterday, he had soreness and tightness. The trainers examined him, and that's the way we're going right now."
Maddon said Reyes' value to the team has been "right up there at the very top."
"Up until this [poor] run offensively, the biggest problem we've had is keeping the other team from scoring late," Maddon said. "And without him being here, our record would not be even as good as it is. He has been that important. So we're going to have to piece it together until he gets back."
The Rays recalled left-hander Jon Switzer from Triple-A Durham on Wednesday.
Maddon planned to use right-hander Gary Glover as his closer on Wednesday and Jay Witasick as his setup man, with Switzer and Casey Fossum used as situational lefties.
Maddon managed an ironic smile when asked how this latest bad news would play with the mind-set of his team.
"It's not one of the better things that could have occurred," Maddon said. "It's just a tough moment. What are you going to do? It just happened. It's just one of those things. It happened and we just have to wait until he gets well. He felt better today than yesterday, that's encouraging."
If all goes well, Reyes would come off the DL on July 18.
Switzer returns: Switzer, who got the news Tuesday night that he would join the team in Boston, woke up at 6:30 a.m. ET Wednesday, caught a direct flight from Raleigh, N.C., to Boston and was at Fenway Park by 11 a.m.
The Rays had several options to chose from at Durham, where Scott Dohmann, Jeff Ridgway, Chad Orvella and Seth McClung are all pitching well.
"The guys who have seen [Switzer] most recently chose Switzer," Maddon said. "He's been very consistent. Throwing 89, 90, 92 -- and last year, when he was in the low 90s, he was very effective actually -- [so it] sounds like his velocity is back. He's been nails."
Switzer, 27, opened the season on the DL with left shoulder tendinitis. He was activated June 2 and assigned to Durham, where he appeared in 17 games with the Bulls, allowing only one earned run in 22 innings. Opponents have hit just .231 against Switzer.
"They've been using me in good situations down there that fit me well," Switzer said. "Like left-on-left matchups, that kind of stuff. And it's just worked out well. I've had a good run."
Switzer said he has thrown a lot of sinkers.
"I've tried to get ground balls as much as possible," he said. "I've been getting lefties out, though I had a rough streak where they got like five hits in seven at-bats. But they weren't hitting the ball hard."
This is the fifth time in the last five seasons Switzer has spent time with the Rays; he made two tours in 2003, spent three weeks with the club in 2005 and the second half of 2006.
Upton update: B.J. Upton (strained left quadriceps) was scheduled to play seven innings for Durham on Wednesday, and the Rays are hoping he'll follow the performance with a nine-inning stint Thursday and a start at designated hitter on Friday before he is re-evaluated Saturday.
Maddon said the chances of Upton returning to the team before the All-Star break are remote and the team will likely keep him playing during the break.
"It isn't that important that he faces Triple-A pitching, just that he plays," Maddon said.
Up next: The Rays will close out their three-game series against the Red Sox on Thursday night in a 7:05 ET contest at Fenway Park. Left-hander J.P. Howell will start for the Rays and will be opposed by right-hander Josh Beckett.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.