All animals at Chester Zoo "are accounted for" following a fire at the Monsoon Forest habitat area, Cheshire Fire and Rescue Service said.
However, the zoo said later that staff were actually still working to account for all the species in the enclosure, although rare orangutans and other mammals had been accounted for.
It also said that an event planned for this evening had been cancelled.
A statement on the zoo's website said: "Critically endangered Sumatran orangutans and other mammals are all accounted for.
"We are working hard to account for all other species."
It added: "The zoo's The Lanterns event this evening has been cancelled and ticket holders notified by email."
Visitors were evacuated after the blaze broke out.
David Clough, 50, who lives across the road, said: "We first saw signs of the fire shortly after 11.30.
" The Monsoon Forest building in the zoo's new Islands development was on fire.
"It has an inflatable roof that was burning. Lots of flames and smoke.
" We were very worried for the people and animals that would have been in the building.
"Orangutans and gibbons are our nearest neighbours there, but there are many other animals, including free-flying birds.
"It was spreading across the roof in strong winds for a while.
"Lots of fire engines arrived quickly.
"By about 30 mins ago the main flames had gone, but there's a smaller fire still burning at the southern end of the roof."
A visitor to the zoo, who did not want to be named, added: "We were in the monsoon enclosure when it happened and were rushed out due to an electrical fire. The 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."
One person has been treated for smoke inhalation.
A spokeswoman for the North West Ambulance Service said it was called to the scene at 11.42am.
"We had two rapid response vehicles and one ambulance on the scene, all of which cleared as there were no patients," she said.
"There is one patient with smoke inhalation. We've got an officer on the scene."
No further details were provided about their condition.
Chester Zoo's sub-tropical Monsoon Forest enclosure is billed as the largest indoor zoo exhibit ever built in the UK.
The enclosure houses animals and fauna native to South East Asia.
Among its residents are Sunda gharial crocodiles, painted batagur turtles, moloch gibbons and rhinoceros hornbills, a type of exotic bird.
The enclosure was opened in 2015 as part of a £40 million development at the the zoo.
The 5,000 square metre area includes raised forest walkways and underwater viewing areas where visitors can see the crocodiles.
It is clad in a giant polymer dome, much of which was destroyed in Saturday's blaze.
The conditions inside mimic the climate in South East Asia.
It also contains exotic plant species including starfruit, mango, paw paw, orchids and palm trees.
Rain is sprinkled from outlets the roof structure and thunder clap sound effects are played out across the enclosure.