The farmer reportedly claimed that the little girl wandered onto his land and was killed after encountering the leopard on his farm.
Egyptian media reported that this was not the first time that dangerous animals had escaped from the farm.
Last year a hyena and a tiger got loose but were recaptured before anyone could be hurt.
Villagers said the farm had a license to raise animals as pets but that the farmer had diverted into bigger and more dangerous creatures in the hopes of selling them to zoos.
After the killing a mob of villagers tried to break into the farm to kill the remaining animals but they were they were forced away by police.
The leopard is believed to have escaped several days before the killing on Sunday and residents said they had seen the animal prowling at the edges of their village in the Giza district.
Videos posted online showed a crowd of children cheering and playing with the leopard's corpse after it had been killed by police.