Cueto was shut down Monday night after three scoreless innings of his start with Class A San Jose, where he was rehabbing because of blisters. He had been scheduled to throw about 70 pitches but was removed after 34.
Tests on Tuesday showed the strain but no damage to the ligament. There is no timetable for his return.
Cueto can opt out of a six-year, $130 million deal this offseason.