About 70 firefighters tackled the blaze at its height in the Animal Adventure section that spread to a shop.
One person was taken to hospital and eight were treated at the scene.
The zoo said an aardvark called Misha died in the fire and four meerkats were still unaccounted for, presumed dead. The zoo was shut on Saturday but said it would reopen on Sunday.
The cause of the fire is not yet known.