Mijares has been on the disabled list since May 15 with a strained left elbow. He started the season as the primary lefty setup man for manager Ron Gardenhire. He has a 5.40 ERA in 18 appearances this year.
The Twins optioned lefty Dusty Hughes to Triple-A Rochester to make room for Mijares. Hughes is 1-0 with a 9.95 ERA in 15 appearances this year.
Gardenhire also said Sunday that an MRI showed inflammation in Joe Nathan's right forearm. Nathan is on the DL with an elbow injury and doctors say the inflammation is common in pitchers returning from Tommy John surgery.