Three zoo workers were reported dead and the AFP news agency reported that eight people in total had died in the floods.
It was not immediately clear if the eight people were killed from the flooding or animal attacks. 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 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.
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 capital.
Source: Agencies