Ohtani was 4-2 with a 3.31 ERA in 10 starts last season. The 24-year-old is not expected to pitch in a game until next spring, according to NBC Sports.
Ohtani missed the season's first six weeks recovering from the surgery. The defending American League Rookie of the Year is hitting .277 with nine home runs and 31 RBIs since returning May 7.
Ohtani had 22 home runs and 61 RBIs in 104 games as a hitter last season. He became only the fourth Japanese player -- and the first since Seattle's Ichiro Suzuki in 2001 -- to win Rookie of the Year.
Ohtani joined Babe Ruth as the only MLB players with 10 pitching appearances and 20 home runs in a single-season.
The Angels are 3 1/2 games behind the Cleveland Indians for the American League's second Wild Card spot.