Mercado suffered the injury while making a diving catch in an exhibition game Thursday against the San Francisco Giants.
Mercado told reporters Sunday that he believes he should be ready to go by Opening Day.
"Yeah, I think so," Mercado said. "I think I should be good by then. I trust my ability to recover and I trust [the training staff] in there."
Mercado, 25, is penciled in for a starting spot in the outfield this year. His versatility will allow manager Terry Francona to play him in any of the three outfield positions, but mostly in center.
Mercado batted .269 with 15 homers and 59 RBIs in 118 games last season.
The Associated Press contributed to this report.