May threw just 27 pitches Saturday before leaving a game the Dodgers eventually lost 6-5 to Milwaukee in 11 innings. After his final pitch, May reacted with obvious pain, took a few steps and called for attention.
After the game, manager Dave Roberts said May felt "kind of a shooting sensation" through his arm on a curveball he threw.
Roberts said Sunday the 23-year-old May would get an MRI when the team arrives in Chicago on Monday to begin a series against the Cubs.
The Dodgers purchased the contract of left-hander Mike Kickham and transferred right-handed reliever Corey Knebel to the 60-day injured list.
May is 1-1 with a 2.74 ERA in five starts this season. He has a career mark of 6-5 with a 2.93 ERA in 31 appearances, including 19 starts.
May joins a crowd of Dodgers pitchers on the injured list that also includes Caleb Ferguson (left elbow surgery), Tony Gonsolin (right shoulder inflammation), Brusdar Graterol (right forearm tightness), Tommy Kahnle (Tommy John surgery), Joe Kelly (shoulder inflammation), Knebel (right lat strain) and David Price (right hamstring strain).
The Dodgers have days off May 10 and May 13. Roberts noted those breaks in the schedule could enable the team to use a four-man rotation for a short period.