The catcher doubled in his first at-bat and then struck out twice.
Ross will likely be activated from the disabled list on Friday.
"He'll get examined tonight and probably tomorrow when he comes in and at that point we have the ability to make a roster decision tomorrow," Red Sox manager John Farrell said.
Morales gave up one unearned run over five innings in his latest rehab start. The left-hander has been on the disabled list since Spring Training, when he was sidelined with a back injury. He then strained a pectoral muscle during an April 17 rehab start.
Morales threw 78 pitches on Thursday, notching three strikeouts and two walks.
Morales could be activated as a reliever for the Red Sox, but because he pitched Thursday, that decision is at least a few days away.
"He's not available for the next four or five days at a minimum," Farrell said. "That will be taken into account over the next couple days in our discussions and what potential moves we might make with him."
Michael Periatt is an associate reporter for MLB.com. Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.