Locals had been told to stay indoors immediately after the flood allowed the animals, including wolves, lions and a hippopotamus, to roam the streets early on Sunday.
Most of the animals had been rounded up by Wednesday but workers who entered a flood-damaged warehouse close to the zoo to clear it up stumbled across the white tiger which killed one of them, the government said.
"One man was attacked by a wild animal. He is dead," Interior Minister Vakhtang Gomelauri told reporters. Police later shot and killed the tiger.
Some 300 animals escaped or died in the floods that also killed at least 19 people. Police killed many animals, including a lion and six wolves but some of the animals were recaptured alive.
A woman called emergency services later on Wednesday to report she had seen the remaining tiger in the city center, but police were unable to find it.
Six people are still missing after the floods that washed away buildings, roads and cars.
The Finance Ministry has estimated the damage at up to 100 million lari ($45 million) and government officials are in touch with international donors to discuss aid.
Some experts said the flood was caused by a landslide that occurred during heavy rains that turned the city's river Vere into a torrent.
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