Misha the aardvark, described as "one of the attraction's best-loved animals", perished in the fire.
London Fire Brigade (LFB) said the fire broke out in a cafe and shop near the Meerkat enclosure and an animal petting area.
The zoo also revealed that four meerkats, whose enclosure was nearest to the fire, were unaccounted for, but they are now presumed dead, as well.
Zoo director Dominic Jermey said the staff was "absolutely devastated" by the aardvark's death.
London Zoo said in a statement: "We have keepers living on site and they, along with our security team, responded incredibly quickly to move animals to safe locations within their enclosures".
The zoo will remain closed on Saturday until further notice.More news: Hip Hop Icon Reggie Osse aka Combat Jack Dead At 48
At its worst, the flames spread to a shop and at one point, 70 firefighters were on the scene battling the fire, which sent one person to the hospital.
TV footage from the scene showed the Adventure Cafe and shop to be badly damaged. However, it confirmed on Twitter it would reopen Sunday.
"It's too soon to speculate on the cause of the fire but we will be working very closely with fire investigators over the coming days and weeks to ascertain the cause".
The alarm was raised shortly after 6:00 am (0600 GMT), and it was not until around 9:30am that the fire was brought under control.
It took 72 firefighters just over three hours to put the fire out.
Zoo: Firefighters dampen down the blaze.