Giolito was cruising early against the Kansas City Royals, with five strikeouts over 2⅔ innings, but he grabbed at his right hamstring while delivering a pitch to Alex Gordon in the third inning. After throwing a couple of warm-up pitches, Giolito was pulled from the game.
He told reporters Thursday that he underwent an MRI, which showed the Grade 1 strain, and added that he thought he could pitch through the injury if it were "a different situation, maybe a different time of year."
Giolito, 24, is 2-1 with a 5.30 ERA over four starts this season.
"It looks like he'll miss a couple starts and get all his treatments done. At that point, we'll reassess how he's doing," manager Rick Renteria said.
ESPN's Bradford Doolittle and The Associated Press contributed to this report.