Misha the aardvark, described as "one of the attraction's best-loved animals", perished in the fire.
TV footage from the scene showed the Adventure Cafe and shop to be badly damaged. "We will update as quickly as the situation allows".
The zoo tweeted: 'ZSL is now dealing with an incident on site. "They worked incredibly hard in arduous conditions to bring it under control as quickly as possible and to stop it from spreading to neighboring animal enclosures".
A statement said: "Fire crews from Kentish Town, Paddington, Euston, West Hampstead and other surrounding fire stations are at the scene". However, it confirmed on Twitter it would reopen Sunday.
It is not yet clear how the fire - which is at the Adventure Cafe Shop - started.
"We will aim to re-open when we know it is safe to do so for animals, staff and visitors".
It WON'T be a white Christmas in Swiss cities this year
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When deputies found her body, they said she had suffered "severe trauma" and was being guarded by the two dogs . It took authorities more than an hour to catch the dogs.