Morales was placed on the 15-day disabled list before Tuesday's game against the Angels with left shoulder inflammation.
Over his last two starts, Morales pitched eight innings while giving up 12 hits and 11 runs, seven of which were earned.
It is unclear when he will return.
"It was a little cranky the other day, and at this time of the year, I just didn't think there was any reason to be anything but cautious," said manager Bobby Valentine.
Morales has pitched in 37 games this season, going 3-4 with a 3.77 ERA. He has started nine games, going 3-3 with a 4.14 ERA while holding opponents to a .225 average.