Police and soldiers were hunting down the animals, recapturing some and shooting others dead, while rescuers airlifted scores of people trapped by the floods.
Prime Minister Irakli Garibashvili called on Tbilisi residents to stay indoors while the animals were still at large, describing the damage to the city's infrastructure as "substantial" after the River Vere burst its banks after hours of torrential rain.
"Our latest estimate is that the death toll is 12," Tbilisi Mayor David Narmania told journalists.
Several main roads were completely destroyed and small houses and cars were swept away by the torrents, while half a dozen coffins in a city cemetery were washed out of the ground and lay on the mud.
Tbilisi Zoo spokeswoman Mzia Sharashidze told the InterPressNews agency that three dead bodies had been found on the grounds of the zoo, including those of two employees.
"Search for animals continues, but a large part of the zoo is simply non-existent. It was turned into a hellish whirlpool," Sharashidze said.
"Only three out of our 17 penguins were saved," she added.
Rustavi 2 television broadcast footage showing a hippo swimming in the flooded Heroes' Square in downtown Tbilisi as rescuers struggled to capture the animal.
The corpses of a lion and a pony lay on the road close to the zoo on this afternoon, an AFP journalist saw.
The government set up a hotline for residents to inform the emergency services if they spotted any of the predators.
"The human losses that we have suffered are very hard to tolerate. I express my condolences to all the people who lost their relatives," Margvelashvili told local television.
Jacob Janjulia, a 21-year-old student who was among the residents volunteering to help rescuers, said parts of Tbilisi were "ravaged".