Morrow, who has been out since June 12 with a strained left oblique, surrendered three hits while striking out two over five innings of work.
The native of California will now make at least one more rehab start for the Fisher Cats before being considered for a return to the big leagues.
"Physically fine, 51 pitches in the five innings," Blue Jays manager John Farrell said. "So the goal was to get him to 65 pitches [Wednesday] night to make his next start about 80-85, which is kind of an ideal number of pitches to get him back to before he gets back to a game here.
"He'll start in another five days and we'll reassess at that point if the number of pitches in his next outing are enough to get him back here, or does he need one additional start prior to being activated."
Farrell said Morrow possessed consistent velocity throughout his outing for New Hampshire and didn't show any ill effects from the injury that has kept him out of action for two months.
Morrow had been the Blue Jays' top pitcher at the time of his injury. He is 7-4 with a 3.01 ERA in 13 starts this season, with 67 strikeouts and 24 walks.