"We fully expect and are hopeful that this will be near the 15 days before he's activated," said manager John Farrell.
Left-handed pitcher Craig Breslow, who missed Spring Training with a left shoulder injury, was activated to take Bailey's spot on the roster.
Bailey will not throw in the upcoming days. Instead, he'll do extra work in the training room as he attempts to keep his arm strength that aided in his 20 strikeouts over 12 1/3 innings. He was 5-for-6 in save chances while posting a 1.46 ERA and holding batters to a .140 average this season.
"One of my personal goals, I've told you 1,000 times, was to stay healthy," Bailey said. "And obviously a 15-day stint isn't great, but it's a little blip on the radar of things we want to do here as a team."
Bailey, who pitched in just 19 games last year, was relieved there was no major damage.
"Obviously, as a player, that part of the body is very delicate," he said. "But knowing I just strained that bicep, I guess it's peace of mind."
"For me, just a couple days of rest, get back throwing and hopefully it's not too far away."
Joel Hanrahan will return to the closer role in Bailey's place. Hanrahan has pitched two innings and allowed one run since his return from a right hamstring injury on April 30. He remains confident that he can be a lock-down closer, even after being demoted to setup duty.
"I still feel like I can be pretty darn good here, and that's all that matters to me," Hanrahan said.
The Red Sox didn't necessarily plan on having two proven closers on their roster this season, but the depth has been an advantage thus far.
"Fortunately in the situation we're finding ourselves in, to have two guys we can build back to to close out games, it's certainly a luxury or a benefit on our part," Farrell said. "But when both guys are healthy, certainly that's our best team."