Morrow has missed almost three months after landing on the disabled list May 3 with shoulder soreness. He signed a one-year deal in the offseason, and he is 2-0 with a 2.73 ERA in five starts this year.
"He's shut down right now," Padres interim manager Pat Murphy said. "We don't know how significant it is and we don't know the extent of it ... but it's certainly not 'all systems go.'"
Morrow appeared ready to return from the disabled list in early June before feeling soreness in a rehab start at Double-A San Antonio. He was shut down for more than an additional month, returning to start for El Paso on Saturday.
Morrow threw 40 pitches and checked out medically before his mid-week bullpen session. He planned to make one more rehab start after Thursday's, a light at the tunnel that now feels farther away.
Myriad injuries -- including left oblique, right forearm and right finger issues -- limited Morrow to just 37 starts over his final three seasons for Toronto.