Orangutans, gibbons, crocodiles, turtles and exotic birds were among the species housed in the artificial habitat designed to mimic a south-east Asian environment.
Keepers were able to save those animals by encouraging mammal species away from the fire - including the zoo's group of critically endangered Sumatran orangutans.
But some insects frogs, fish and small birds were killed near the outbreak of the fire.
A spokesman for Chester Zoo said: "Visitors were evacuated immediately and we would like to thank them for their understanding and cooperation. Thankfully, no staff or public were harmed in the incident.
"Keepers were able to encourage all mammal species away from the fire and to safety - including the zoo’s group of critically endangered Sumatran orangutans, Sulawesi macaques, endangered silvery gibbons and birds such as rhinoceros hornbills.
"We are though, devastated to say that we were unable to save some of our insects, frogs, fish and small birds who were located near to the outbreak of the fire. It’s absolutely heart-breaking to lose any animal, especially when conservationists have worked so hard to breed these wonderful species.
"New homes have been found within the zoo for all of the animals that were led to safety and our teams are working around the clock to relocate them as soon as possible."
The zoo said it had been inundated with messages from people asking how they could lend their support.
"We remain committed to our mission to prevent extinction and for those who're asking how they can help, we would welcome a donation to our continuing conservation work," the zoo said.
A justgiving fundraising page had received more than Â£8,000 in donations on Sunday.
Cheshire Fire and Rescue Service declared a major incident after it was called to the zoo shortly before 11.30am.
Eyewitnesses described how visitors to the attraction - billed as the largest indoor zoo exhibit in the UK - were rushed to safety as the blaze spread rapidly through the polymer roofing material.
Meanwhile zoo staff led the animals housed in the structure to safety as firefighters arrived on the scene.
One person was treated for smoke inhalation as a result of the fire, according to North West Ambulance Service.
One eyewitness, David Clough, 50, who lives across the road from the zoo, said high winds fanned the flames in the roof of the building.
He added: "We were very worried for the people and animals that would have been in the building."
He added: "Orangutans and gibbons are our nearest neighbours there, but there are many other animals, including free-flying birds."
A visitor, who declined to be named, told the Press Association: "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."