Manager Terry Francona said when Beckett is able to resume his usual long toss routine leading up to his next start, then the team will be confident the 31-year-old right-hander is ready to go.
"He's doing much better today," Francona said. "He can do his throwing and things like that, so he's not going to get sent back. He gets looked at every day. We all know how important his five-day schedule is, so when we think we get to that point, then we'll slot him in."
Francona said Bedard would rejoin the team in St. Petersburg sometime this weekend.
Francona said the problem flared up in Bedard's last start, when the 32-year-old allowed three runs on five hits in a 12-7 win over the Rangers.
"He was throwing all arm, and as we got through that start, it started to flare up on him a little bit," Francona said. "We'll slot him in when we think it's appropriate."
The problem could have occurred from Bedard overcompensating for lingering issues with his left knee, which was sprained earlier in the year when he was with the Mariners, said Francona.