At least 10 people have been killed in the disaster, including three zoo workers.
An escaped hippo was cornered in one of the city's main squares and subdued with a tranquilizer gun, the zoo said.
Some other animals also have been seized, but it remained unclear how many are on the loose. Bears and wolves are also among the animals who fled from their enclosures amid the flooding from heavy rains and high winds.
Heavy rains and wind hit Tbilisi during the night, turning a normally small stream that runs through the hilly city into a surging river. The flooding also damaged dozens of houses. City mayor David Narmania told journalists that 10 people were known to have died; 10 others were reported missing.
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Helicopters are circling the city and residents have been told to stay indoors except in an emergency. About 1.1 million people live in the former Soviet republic's capital.
"When Communists came to us in this country, they ordered that all crosses and bells of the churches be melted down and the money used to build the zoo," he said.
"The sin will not go without punishment. I am very sorry that Georgians fell so that a zoo was built at the expense of destroyed churches.