Bourn left Saturday's 2-0 win over the White Sox when he felt the leg tighten after beating out a bunt single.
Bourn, hitting leadoff, struck out in his first at-bat on Thursday. The 31-year-old, two-time All-Star had surgery on the hamstring in October and then strained it during spring training. He missed the first 13 games of the season while on the disabled list.
Thursday is only Bourn's 16th game played this season. He is hitting .266 with no homers, four RBIs and two steals in five attempts.
Nyjer Morgan, who has filled in for Bourn, is expected to remain with the team through an upcoming trip to Tampa Bay and Toronto, where the Indians will play on artificial turf.
A nine-year veteran of the Phillies, Astros, Braves and Indians, Bourn has 301 career steals. SI WIRE: Report: Pirates prospect Gregory Polanco turned down 10-year contract