The fire broke out in the roof of the Monsoon Forest habitat, which led to an evacuation of visitors. The zoo said the cause of the fire is unknown.
All mammals including critically endangered Sumatran orangutans, Sulawesi macaques, endangered silvery gibbons, and birds such as rhinoceros hornbills were saved from the blaze.
However some insects, frogs, fish and small birds who were located near to the outbreak of the fire could not be rescued.
A fundraising campaign set up by the zoo on Sunday after the fire reached its £50,000 target within hours.
The zoo said it was "one of the toughest days in its history".
In a statement, it said: "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 popular tourist attraction, which is home to more than 21,000 animals, it will be working to rebuild this part of the zoo and "continue our mission of preventing extinction".
Jamie Christon, the zoo's chief operating officer, said: "Yesterday was one of the toughest days in Chester Zoo's long history.
"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."
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.
Lee Shears, incident commander at Cheshire Fire and Rescue said: “It was a challenging experience and a large and complex fire.
“We had in excess of 15 pumps and we’ve managed to enter the building and contain the fire in a short space of time. We’ve managed to save a significant portion of the building. It was a good multi agency team approach working with colleagues looking after the safety of the animals.
“Crews are still on site and we’re still damping down. We’re very confident that we know the location the fire started in and we are confident that it is an accidental cause.
Following the fire, the zoo set up a fundraising website appealing for £50,000 towards its conservation work.
Mr Christon added: "The strength and support from the public has been incredibly overwhelming and the messages of goodwill have been of great comfort to our teams.
"We will support each other in rebuilding this part of the zoo and continue our mission of preventing extinction."