He'll have to make at least one rehab start after that and potentially more before he can return to the Majors.
"We want him to have a rehab start or starts, but we want to make sure he'll get through this whole thing and we'll reevaluate after that," manager Joe Maddon said.
Cobb was originally sidelined with a concussion when he was hit in the head with a line drive by Kansas City's Eric Hosmer on June 15 and left on a stretcher.
He was on track for a quick recovery, but a blister forced him out of a rehab start July 23.
Cobb was 6-2 with a 3.01 ERA before the injury, but the Rays have fared well in his absence.
Tampa Bay's rotation has been a big reason the Rays have been able to win 21 of their last 25 games.
"It's kind of interesting and unique that we've been able to recover with [Cobb] being out this long," Maddon said.
Michael Periatt is an associate reporter for MLB.com. Follow him on Twitter @Michael Periatt. This story was not subject to the approval of Major League Baseball or its clubs.