Just five weeks earlier staff had been delighted by the arrival of the baby as part of an international captive breeding programme.
It was described as ‘looking strong’ when it was born to parents Sirana and Nato.
Bristol Zoo said yesterday: “It is with great sadness that we announce the loss of our baby pygmy hippo.
“The five week old calf became ill overnight on Wednesday and was being treated by our vet team.
“Unfortunately, despite their best efforts, the youngster passed away yesterday.
“This is a very upsetting time for our keepers and we know you will all share in our sadness.”
Pygmy hippos are endangered in the wild where there are thought to be fewer than 2,000 in their native west Africa.
The female baby hippo – who had not yet been named by the zoo – died of gastric lactobezoar, a build-up of milk and mucus in the stomach.
Vets tried to save her after she started vomiting on Thursday morning.
Her mother Sirana is being closely watched by zoo keepers who described her as “relatively calm”.
At birth, pygmy hippos weigh 4.5-6.2 kg (9.9-13.7 lb) with males about 0.25 kg (0.55 lb) heavier than females.
They are fully weaned between six and eight months. Until then their mother leaves them hidden as she goes to forage and returns to suckle them around three times a day.
There are thought to be fewer than 3,000 (corr) in the wild.
Their existence is threatened by poachers who hunt them for their meat, especially in Liberia where they are most numerous.