Roberts left during Thursday's 6-3 victory over the Tampa Bay Rays after feeling a pop in his right hamstring near the back of his knee while trying to steal second base.
The team announced Friday they have placed Roberts on the 15-day disabled list.
Roberts was 5-for-12 this season before the injury. Ryan Flaherty and Alexi Casilla will fill in at second base while he recovers. Roberts, 35, has had trouble staying healthy over the past few seasons. He played in 17 games last season, 39 in 2011 and 59 in 2010.