Heavy rains and wind hit Tbilisi overnight on Saturday, turning a normally small stream that runs through the hilly city into a surging river. Officials said 12 people were known to have died and about two dozen others were missing.
The surging floodwater destroyed enclosures at the zoo, killing some animals and letting loose others.
Georgian Culture Minister Mikheil Giorgadze told NBC News: "The special forces are doing everything to control the situation. We are all mobilized"
It wasn't immediately clear if any of the people killed were attacked by animals.
Three zoo workers were killed in the floods, the zoo said. One of them was Guliko Chitadze, a zookeeper who lost an arm in an attack by a tiger last month.
Helicopters were circling the city and residents were told to stay indoors except in case of an emergency.
A spokeswoman for the zoo said that many of the animals were killed in the flooding or by special forces, but it was not known how many remained at large.
"Not many animals are still on the loose but it is difficult to say how many are still out there," Mzia Sharashidze said.
Footage from Tbilisi showed a hippopotamus roaming the streets, while a bear could be seen climbing around an apartment window. The hippo was cornered in one of the city's main squares and subdued with a tranquilizer gun, the zoo said.
Six wolves were shot dead in a yard at an infectious diseases hospital, while there where images of a dead lion, hyena, and a wolf — all presumably drowned in the floods.
Some officials accused authorities of using unnecessary force against the wild beasts. Zoo director Zurab Gurielidze said one of the park's most beloved attractions, a young white lion named Shumba, had been found shot in the head.
"Our Shumba is no more," he lamented, according to the news agency Interfax. "It's simply possible that someone exceeded his authority." The flooding damaged dozens of houses and left streets covered in mud and debris. Images showed several cars upturned and a fire truck left swamped in the detritus.
Georgia's Environment Minister Gigla Agulashvili said forecasts showed there could be a repeat of Saturday night's rain, and rescue work would stop at nightfall Sunday "to avoid further loss."
Prime Minister Irakli Garibashvili announced the nation day of mourning was on Monday. Finance Minister Nodar Khaduri estimated the damage bill was $20 million. About 1.1 million people live in the former Soviet republic's capital.
The head of the Georgian Orthodox Church, Patriarch Ilia II, was quoted by the Interfax news agency as telling a Sunday Mass that Georgia's former Communist rulers bear responsibility for the disaster.
"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."