Samardzija underwent an MRI on Thursday that revealed the injury. Manager Bruce Bochy said he will rest 10 days and then begin throwing.
Samardzija left a minor league outing on Wednesday after allowing two home runs and a double in a rocky fourth inning.
Samardzija, who was expected to be the Giants' No. 3 starter after Madison Bumgarner and Johnny Cueto, had a 10.64 ERA in four Cactus League starts. His fastball velocity has been around 89-90 rather than his normal 93-94, Bochy said.
Left-hander Derek Holland, a non-roster invitee to camp, is the most likely candidate to replace Samardzija in the rotation to begin the season.