Cueto recently met with team doctors regarding a sore elbow.
Two days after saying there was a "strong possibility" Cueto would need the surgery, Giants manager Bruce Bochy said the injury has "been lingering quite a while."
The 32-year-old is winless in four starts since returning from a two-month stint on the disabled list with an elbow injury following a strong start to the season. He is 3-2 overall with a 3.23 ERA in 53 innings.
After signing a six-year, $130 million free-agent deal, Cueto had a strong first season in San Francisco in 2016, going 18-5 with a 2.79 ERA.
But he has struggled with injuries since, limited to 147 1/3 innings in 2017 when he was 8-8 with a 4.52 ERA.