Upson tore fibres in his calf and hobbled off the Anfield pitch 15 minutes from the end of last weekends 3-1 defeat against Liverpool.
Although the injury is not considered too serious, the game against Rovers at St. Andrew's will probably have come to early for the England international centre-back to take his place in Steve Bruce's side.
Either Darren Purse or Olivier Tebily will partner Kenny Cunningham in Upson's absence.
