The veteran left Wednesday's game with tightness in his left hamstring after recording the first two outs in the bottom of the ninth inning. The Rays went on to win, 5-3, over Texas, but not before Percival made his exit, walking off the mound under his own power.
Percival, 38, has recorded 14 saves on the year and has been a big part of the Rays' early-season success.
"It's a huge loss," reliever Dan Wheeler said. "What he's been able to do for us this year, on and off the field, it's invaluable."
Percival, while understandably upset, said he had been fighting hamstring problems since Spring Training and again in Oakland last week, but did not feel like he hit a nerve in his leg until Wednesday's game.
"I understand they are looking out for the best of the Rays and the best for me, [but] I don't have to agree on it," Percival said.
"I knew I was going to unavailable for probably four or five days ... so it just gives me a little extra time."
The right-hander expects to throw off a mound within a week, and still will accompany the Rays on their upcoming nine-game road trip.
"For two weeks we can pick up Percy, and let him pick us up the rest of the season," said Maddon, adding that he would not name a replacement for Percival.
Instead, the Rays will go with a combination of Al Reyes and Wheeler, the late-innings guys, in addition to relievers J.P. Howell, Gary Glover and lefty specialist Trever Miller.
Maddon said with the strong performances out of the bullpen, he had no qualms about using any of the aforementioned arms to help close.
"Hopefully we can continue to keep going, putting ourselves in positions to win every night," Wheeler said. "Which we are doing right now."
Reyes, who assumed the closer role last season, had 26 saves in 30 opportunities, and Wheeler was a closer with the Astros for parts of last season.
While Wheeler said closing experience helps, the hurler also said that all of the bullpen arms are ready at any time, regardless of the inning.
"You get up when Joe [Maddon] tells you to get up," he said.
While Aybar is expected to remain with the Rays, Maddon said the current move was "temporary" as the club would make make another move to add another pitcher to the bullpen.
Percival, meanwhile, is confident that a few days of rest is all his leg needs to get back into fighting form.
"I took no time this spring when I did it, I just taped it up and kept going," he said. "And I made it this far. So, I think so give me two weeks, I'll definitely have enough time to get some strength built into it."
After a 5-1 loss to the White Sox on Thursday, the Rays bolstered their bullpen by optioning infielder Ben Zobrist to Triple-A Durham and recalling right-hander Grant Balfour.
Balfour was virtually unhittable in Durham, going 1-0 with a 0.38 ERA and collecting eight saves in 15 appearances. Opponents at Triple-A were hitting just .067 off Balfour, and the righty allowed just one run in 23 2/3 innings. With the move, Balfour is expected to slide into the Rays bullpen as the 12th pitcher on the staff.