Jade, a two-year-old female Amur leopard, was being transferred into a new enclosure at Marwell Zoo with three-year-old male Akin.
She managed to climb a tree, and squeeze through a small opening in the mesh over her new home.
Staff from the zoo surrounded her tree, and she was shot with a tranquilizer dart. Unfortunately, after being knocked out, she did not come round.
Zoo staff aren't sure exactly why she died, but are very upset.
There are only about 33 Amur leopards left in the wild, and 105 in captivity in Europe.
79 of these are in breeding programmes, which hope one day to be able to reintroduce these beautiful cats to their native home in Russia.