The Cardinals will have pitcher Joe Kelly make at least two more minor-league rehab starts before he returns from the disabled list, according to MLB.com.

Though Kelly has put the injury behind him, the team wants him to build up his pitch count before bringing him back. He threw 49 pitches in his previous outing, and manager Mike Matheny said he wants to see Kelly throw 70 pitches Sunday for Triple-A Memphis and 85 in his final start.

Kelly sill likely be activated shortly after the All-Star break. Kelly has not pitched since April 16 as a result of the injury.