Bourn, who signed a four-year contract worth $48 million with the Indians in February 2013, underwent surgery on the same hamstring in October.
Expected to be the club's Opening Day center fielder, Bourn is batting .214 this spring in 28 at-bats. He went 1-for-2 on Sunday with a run scored.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. Tyler Emerick is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.