The Graves Park Animal Farm shop in Graves Park was broken into overnight on Sunday.
It took members of staff five hours to clear up the wreckage, with animal food and items for sale left strewn across the floor.
It has not yet been disclosed if anything was stolen, but two British giant rabbits were taken from their cage in an attempted theft.
They were found under a nearby shed, with their cage door open.
A police probe is underway.
An animal farm spokesman said: "It has just taken our staff over five hours to clean up the mess. The police have been and crime scene investigation.
"Someone will know who has done this. Please help by spreading the word.
"Also, our British giant rabbits, Olivia and Francesca, were broken into and stolen. We have just found them hiding under a shed near the pigs, cold and very frightened. Someone must have dropped them when they left."
Anyone with information should call South Yorkshire Police on 101.