In a Facebook post, the zoo, which has now been closed, confirmed: "The zoo's animal teams are working to move all animals away from the incident."
Footage online shows huge plumes of smoke coming from the top of a building.
The zoo said the fire brigade are attending the fire which has broken out at the Monsoon Forest habitat.
It is the largest indoor zoo exhibit in UK history, according to Chester Zoo, and is home to tropical animals and plants.
Crocodiles, monkeys and exotic birds are among the animals housed in the exhibit.
David Clough, 50, who lives across the road from the zoo, said high winds fanned the flames in the inflatable roof of the building, adding: "We were very worried for the people and animals that would have been in the building."
One woman, who was at the zoo during the evacuation, told Sky News: "We were inside the building when we heard the alarm go off and we were told to go outside. Everyone was really calm.
"We had to evacuate and watched the orangutans come out of the building. I think it was a mum, dad and two baby orangutans. Two of them were holding their blankets.
"Then we watched the building go up in smoke."
She added: "There were other animals in there; some flightless birds, frogs, ladybirds and a crocodile."
Another visitor said: "We were in the Monsoon enclosure when it happened and were rushed out due to an electrical
fire. It spread very quickly.
"The staff ensured all the members of the public were safe. Many staff (were) running towards the fire, (I'm) assuming to help with evacuating animals.
"The entire zoo is closed – a shame as we've travelled up from Plymouth."
Chester Zoo is home to 21,000 animals.
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Last year, five animals died in a blaze which had to be tackled by 72 firefighters at London Zoo.