Gomez was not previously on the 40-man roster, so to select his contract, the Red Sox moved Jacoby Ellsbury (right shoulder) to the 60-day disabled list, which means the soonest he can return is June 13.
McDonald last played Friday in a 7-5 win over the Indians, striking out in a seventh-inning pinch-hit appearance, and he pitched on May 6, but said the injury wasn't tied to one event. An MRI revealed the strain.
"One of them things, I've just been trying to battle through it for a while," McDonald said. "It's better for the team myself to get it 100 percent. Just get it ready, instead of just letting it nag."
Asked specifically if pitching had an affect, McDonald laughed: "My whole body was sore after that," he said.
"I asked him today when it happened, he said, 'You should have known when I didn't get around on a 90-mph fastball,'" manager Bobby Valentine said. "He worked through it, then didn't play and it felt better, just never really got better."
McDonald is hitting .179 with a .277 on-base percentage and a pair of home runs in 26 games and 56 at-bats.
Gomez, from the Dominican Republic, is a right-handed bat who hit 10 home runs with a .294/.336/.610 line in 34 games with Pawtucket. He came on Sunday in the eighth inning as a defensive replacement at first base and struck out in his first at-bat, against right-hander Jairo Ascensio, ripping one pitch hard foul.
"Well, we were hoping to get the ball [from a first hit] of course, but it's always fun to see the first," manager Bobby Valentine said. "That was his first at-bat and he had a bounce in his step."
The Red Sox signed Gomez as a Minor League free agent on Feb. 2. Last season in the Braves' organization was his first at Triple-A, and although it took until his eighth pro season to get there, he made the most of the opportunity. He led the International League in total bases (264) and was second in hits (154) and extra-base hits (60). He hit 24 homers with a .304/.356/.522 line.
Gomez's pro career began when he was 19, in 2004, with the Rangers' organization.