Lefty Roenis Elias, who pitched the final two innings of Sunday's 16-2 romp over the D-backs, was optioned back to Triple-A Pawtucket.
Due to the fact Pawtucket was involved in the late stages of a doubleheader as the Red Sox were getting ready to board their flight to Cleveland, the corresponding roster moves have not been made yet.
Clay Buchholz will again start in place of Wright on Thursday. Wright is suffering from bursitis in his right shoulder caused when he dove back into second as a pinch-runner on Aug. 7.
"It's just not progressing the way I thought it was going to. It just hurts," Wright said. "I don't want to go out there and throw with too much pain, because I don't want to start compensating. If it's hurting as much as it has been on flat ground, you start adding the mound and all that, adrenaline, the last thing I want to do is hurt myself even more."
There's still a chance Wright could be activated to start on Aug. 23 at Tropicana Field, when his turn in the rotation would come up again.
"I'm super confident," Wright said when asked if he felt the injury would be short-term. "The stuff that I've been doing with the trainers from the first time when I came in on Tuesday until now, it's been significant gains. It's just not where we need it to be. Now that we can take a couple of extra days to really get after it, I'm sure I'll be fine."
With Ramirez out of the mix for the one-game trip to Cleveland and two games in Baltimore, the Red Sox can start Travis Shaw at first base and Aaron Hill at third. Brock Holt can also play both spots.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.