The missing animals include tigers, lions, bears and wolves. Three of the dead people were found within the zoo.
A hippopotamus was cornered in one of the city’s main squares and subdued with a tranquiliser gun.
Rescue workers are searching submerged homes to check for trapped residents.
Dozens of people have been left homeless.
People have been told to stay indoors until the animals have been found
The flooding began when heavy rains caused the River Vere to burst its banks.
Thousands of people have been left without water and electricity while others have had to be airlifted to safety.
Mayor Davit Narmania said the situation was “very grave”.
Georgia’s Prime Minister Irakli Garibashvili has called on residents to stay indoors until the animals have been found.
The hippopotamus was tranquilised, but some animals have been killed
Some have been recaptured or killed though it is unclear how many are missing. Helicopters are now circling the city as part of a search and rescue operation.
Tbilisi’s vice-mayor, Irakly Lekvinadze, estimated the preliminary damage at $10m (£6.43m).
In May 2012, five people were killed in Tbilisi after another river flooded.