In a Facebook post, the zoo wrote that two chimpanzees named Bally and Limbo were "only slightly injured" and were being cared for by veterinarians at the zoo.
Kidogo the gorilla also survived and was doing well, according to the tweet from the city.
"We would like to thank you on this way for the overwhelming wave of compassion and assistance that reach us on all channels," the zoo wrote in a post in German. "We also thank you for the solidarity in social networks. We read everything, but we can't manage to respond to it yet."
The cause of the fire was not immediately clear. The Facebook post went on to say that the monkey house was at risk of collapsing and that it had been cordoned off by fire experts and the police.