Officials say that the victim died at the scene while another man was injured.
Initial reports stated the animal was a lion but it is now believed to have been a white tiger.
A local TV station said the animal jumped on his first victim as he entered a warehouse where it was hiding
The attack happened near Laguna Vere, a open-air swimming pool, and Heroes' Square, just down the road from Tbilisi Zoo.
Police arrived at the scene, but the lion was nowhere to be seen.
A SWAT team was mobilised and a search operation was immediately launched.
It is understood the animal has now been shot dead.
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