Morrow began having a light catch on Monday. He is expected to throw every other day, but there is still no timetable for his return.
"If there was pain, we wouldn't throw him," manager John Farrell said. "The symptoms are continuing to subside. Now we've got to gradually increase the intensity. That will be a slow process, not, you know, risk any kind of setback."
Morrow was enjoying a breakout season prior to the unfortunate injury. He is 7-4 with a 3.01 ERA while also recording three shutouts in 13 starts.
The 27-year-old is currently working out at the club's Minor League complex in Dunedin, Fla. He isn't expected to be ready for a return to the Majors until at least late July.
"It's more just getting his arm moving again," Farrell said. "Naturally there's going to be a little rotation involved there with the throwing motion, but we're not overloading it by any means."