Morrow threw his first bullpen on Thursday at Petco Park, when he threw 32 pitches. He was able to increase his workload and intensity on Sunday.
Morrow said he would throw a simulated game to several of the team's hitters either before Wednesday's game in Anaheim or on Thursday when the team returns to Petco Park.
The next step would be a rehabilitation stint with one of the Padres' Minor League affiliates, where he would likely need two starts before the team reinstates him from the DL.
Morrow had hoped to be closer to returning by now, but it took a little longer to get the inflammation out of his shoulder than he expected.
"The initial soreness took a week [to get over] instead of three or four days," Morrow said.
Morrow was 2-0 with a 2.73 ERA in his first five starts before developing inflammation in his last start on May 2 against the Rockies.
Odrisamer Despaigne has taken Morrow's spot in the rotation and has gone 0-3 with a 10.93 in three starts, though he allowed two runs in six innings the last time out against the Cubs on Thursday.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.