The white tiger had been hiding in a warehouse and escaped the citywide police search for the escaped animals, many of which were shot dead.
The tiger killed the man and injured another in the residential area of Laguna Vere.
"A lion from the Tbilisi zoo killed a man" near the central square, the interior ministry spokeswoman told AFP. "Police special forces were deployed and are hunting down the animal," she said.
"It was a white tiger, a big one. It attacked a man, it seized him by the throat," one agitated eyewitness told the Imedi channel.
Floods hit Tbilisi on Sunday, killing at least 17 people and ravaging the city`s central districts including the zoo, where hundreds of animals - including lions, tigers, wolves and a hippo escaped.
Over half of the animals - some 300 species - either drowned in the muddy waters or were killed by police.
Up to 20 people are still missing after devastating floods killed at least a dozen people in the Georgian capital Tbilisi.
The government of the ex-Soviet republic said the death toll after the Vere river burst its banks on Sunday following hours of torrential rain stood at 12 on Monday morning.
Twenty people were missing as of Monday morning, Manana Tokmajishvili, prime minister Irakli Garibashvili`s spokesman, told AFP, with the death toll expected to rise following Georgia`s worst flood in decades.
The torrents ravaged a zoo in the Georgian capital, with many animals including penguins drowning in the muddy waters.
Other animals such as lions, tigers and even a hippopotamus escaped and were either recaptured or shot dead by police.
Khatia Basilashvili, a zoo spokesman, said four lions, three tigers and two jaguars were killed either in the flood or when on the loose, while the fate of four lions, three tigers and one jaguar was not yet known.
The hunt was still going on for the animals on Monday, Mzia Sharashidze, Tbilisi zoo spokesman, told journalists.
"The search for animals is still underway," she said, adding that some 300 animals had died.
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