Morrow began the season as Toronto's No. 2 starter and went 2-3 with a 5.63 ERA in 10 starts. He left a May 28 outing against Atlanta after two innings and hasn't pitched since.
Anthopoulos said Morrow has been throwing bullpen sessions at Toronto's spring training facility on Florida, but continues to feel discomfort.
Morrow has undergone multiple MRI exams, which have revealed only inflammation.
Anthopoulos also said that left-hander J.A. Happ, who hasn't pitched since being struck in the head by a line drive on May 7 at Tampa Bay, could rejoin the Blue Jays after one more rehab start with Triple-A Buffalo.