Beckett is nursing a stiff back and left his last outing Tuesday against the Tigers in the third inning with back spasms.
"Josh feels much better today but is not going to throw and so he will not pitch on Sunday but it looks like he's feeling better," Red Sox manager Bobby Valentine said before Friday's game against Minnesota.
The Red Sox are unsure when Beckett (5-9) will make his next start.
"I don't think Monday, I don't know about Tuesday," Valentine said. "He might miss a whole start or we might slot him in, we're trying to see how everybody else fits with Josh's recovery but he has not thrown a ball yet so it's hard to say when he's going to pitch in a game."
Will the club put the right-hander on the disabled list?
"It's kind of nebulous but it seems unlikely," Valentine said. "He worked out but he's still stiff."
Morales made five starts earlier this year, going 2-1 with a 3.42 ERA. The left-hander has moved between the bullpen and rotation since Beckett went on the DL in June with right shoulder inflammation. Each of Morales' last five outings came in relief.
Austin Laymance is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.