Residents of Georgia's capital have been warned to stay indoors after heavy flooding destroyed enclosures at Tbilisi's zoo, allowing tigers, lions, bears, wolves and other animals to escape.

Three zoo workers were reported dead and the AFP news agency reported that at least nine people had died in the floods.

The zoo said one of the dead was Guliko Chitadze, a zookeeper who lost an arm in an attack by a tiger last month.

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.

The zoo's press service said on Sunday morning that an escaped hippopotamus was cornered in one of Tbilisi's main squares and subdued with a tranquiliser gun.

Some other animals have also been captured by police while others were shot dead, according to the mayor's office. It remains unclear how many are on the loose.

Paul Rimple, a journalist based in Tbilisi, said the zoo estimated that around half of its 600 mammals, fish and birds had fled their enclosures amid the flooding from heavy rains and high winds.

"It's so surreal. Helicopters are circling overhead and they've warned people to stay indoors but not everyone's doing that," Rimple said.

"People are walking around with their babies just a few blocks from where a wolf was shot in the south of the city. Apparently a jaguar was reported in the north.

"Until somebody gets mauled or killed, no one's going to panic."

Rimple said the authorities were shooting animals they regarded as a danger to the public.

About 1.1 million people live in the capital.