The rabbits were found in a large cardboard box in an alleyway near Landseer Drive, Gleadless on Saturday morning (March 17) and were taken in by a member of the public, who called the RSPCA.
Twenty of the abandoned animals were newborn babies and nine of them have since died.
RSPCA animal welfare officer (AWO) Liz Braidley said: “Some of the rabbits had been fighting and a couple of the adults had sustained quite bad bite injuries as a result. Even one of the tiny babies had been bitten.
“One of the adults has severely infected eyes which appear to be from bite wounds sustained earlier, and is suffering a great deal as a result.
“We have lost so many of the babies it’s heartbreaking. They were so cold and underweight you could see their backbones.”
Liz and colleague RSPCA inspector Kim Greaves are currently caring for the rabbits in their own homes.
She said: “They are in a horrendous state. They are having to be heavily medicated. Their injuries are having to be bathed. Some of them may have long term damage to their eyes.
“The weather was terrible on Saturday, it was freezing cold blizzard conditions. They would have all died if they hadn’t been found.
“The ones that have made it this far are doing okay. We’ll get them right. They won’t be going anywhere until we do.
“If you saw anything, or know someone who had a large number of rabbits but now suddenly doesn’t, then please get in touch.”
Anyone with any information about who owns the rabbits is asked to call the RSPCA appeal line on 0300 123 8018 and leave a message for Liz Braidley.