West Yorkshire Police's wildlife team said that the cat was stolen from her home in Neville Avenue on November 25.
The cat, which was a Bengal named Sansa, was found dead just off Halton Moor Round on Tuesday, November 30.
Officers said the cat was both drowned and shot.
A spokesman for the WYP wildlife team said: "On the 25th November Sansa a Bengal cat went missing from her home address on Neville Avenue, at Leeds.
"Sadly she was found yesterday in a bag on rough ground off Halton Moor Road.
"She had been shot and drowned."
Police are asking anyone with information to contact them via 101 and quote crime number 13210621011.