The tiny creature has been named Winnie, and was born to mother Sirana and father Nato - who are apparently fiercely protective of the new arrival.
There are less than 2,000 of these hippos left in the wild, so the birth is definitely a cause for celebration.
In her enclosure in Bristol, winnie has access to a heated pool, plenty of food and the added benefit of no predators - but her mother's protection instincts are still strong.
A spokesperson for the zoo said: 'Sirana is very protective and doesn't let her stay in deep water for too long. Young hippos tire easily and Sirana will quite often guide her baby into shallow water.'
Winnie has the potential to grow as big as 40-50 stone, and although that might sound too pygmy to you or I, is actually only a tenth of the common hippopotamus - which can reach a whopping 472 stone.
Bristol Zoo Gardens are involved in an international breeding programme for the hippos - but struggle because females only breed once every two years.