Red Sox manager Alex Cora said Martinez tweaked his back running the bases in the third inning.
"He's doing OK," Cora said. "Probably going to be a tough flight [back to Boston] for him. We'll know a little bit more tomorrow."
The Red Sox open a three-game series with the Tampa Bay Rays at Fenway Park on Friday.
Martinez struggled with back spasms last month, missing four consecutive games. He also missed two games in April.
Martinez had doubled in his previous at-bat Thursday and scored a run on Rafael Devers' single in the third inning.
Martinez drove in 130 runs to lead the American League last season, and he batted .330, second in the AL to teammate Mookie Betts. He is batting .296 with 12 home runs and 33 RBIs this season.