However, manager Joe Maddon did not rule out the possibility of Upton returning for Thursday's series finale against the Blue Jays.
Upton was scheduled to play at Double-A Montgomery on Tuesday, but the game was postponed with a doubleheader scheduled for Wednesday.
"I guess he's going to play a game, DH a game." Maddon said. "He's still on pace to get here. He could be here [Thursday], he could be here the next day. I'm not quite sure yet. I'm still waiting to hear from the office to see what everybody thinks.
"It's not really going to kick it back too far."
Upton was 2-for-4 with an RBI for Montgomery on Monday.
Upton was placed on the disabled list on April 4 retroactive to March 26. He has been out since March 14 after an outfield collision with Desmond Jennings.