Middleton is seeking a second opinion, the team said.
He has been placed on the 10-day disabled list. Right-hander Felix Pena was recalled from Triple-A Salt Lake.
Middleton, 24, was removed from Sunday's game against the Twins in the top of the eighth inning because of elbow discomfort with a 1-1 count on Minnesota's Eddie Rosario.
Middleton had just returned from the disabled list last Thursday after being sidelined with elbow inflammation.
He leads the Angels with six saves. He has a 2.04 ERA in 17⅔ innings over 16 appearances, with 16 strikeouts and nine walks.