One animal was in such poor condition he had to be put to sleep, the charity said.
Officers were alerted after the pets were discovered in cardboard boxes at a lane between Allan Street and Mitchell Street.
Two females had been left in one box while a male was in another.
The rabbits were taken to the Scottish SPCA's Lanarkshire Animal Rescue and Rehoming Centre in Hamilton for veterinary treatment and care.
The male rabbit was suffering from severe dental disease which was causing him a great deal of pain and affected one of his eyes.
Last week the Evening Times revealed the Scottish SPCA was investigating after heartless thugs threw a rabbit down a 17-storey rubbish chute.
The animal was found at a block of flats in Maryhill.