The animal was later shot dead, the Georgian interior ministry says.
The tiger was one of several to break free from enclosures at Tbilisi Zoo last weekend following severe flooding.
Georgian police said they tracked the tiger to a disused warehouse but could not sedate it because it was too aggressive.
The flash floods devastated parts of Tbilisi, claiming the lives of 13 people, including three zoo keepers.
There was uncertainty on June 17 about the number of dangerous animals still on the loose, with reports on Twitter of another tiger being cornered in a city centre cafe after the first was shot dead.
The zoo had said on June 16 that all of the missing lions and tigers had been found dead, with one jaguar unaccounted for – sparking confusion when news of the tiger attack on the two men emerged.
Internal Affairs Minister Vakhtang Gomelauri told the press that the animal was found “hiding in an unused store room”.
“We tried our best to sedate the tiger, but it was not possible because the animal was too aggressive. So unfortunately we had to liquidate it,” he said.
Special police units drafted in to deal with the threat posed by dangerous animals have faced criticism, with zoo workers alleging that animals have been killed unnecessarily.
The zoo’s website says two white Bengali tigers live at the facility, one male and one female.
The flash floods devastated parts of Tbilisi, claiming the lives of 13 people, including three zoo keepers.
Up to six people are still missing and about 40 families lost their homes.
Hundreds of volunteers took to the streets on June 17 to help clear up the mess left by the floodwater.
The volunteers, many dressed in trainers and ordinary clothes and armed only with shovels, helped dig animals from the mud and carry them away.
Hundreds of animals drowned when the zoo was swamped by floodwater, while many others escaped.
Lions, hippos and bears were pictured roaming the streets, with residents urged to stay indoors and avoid contact with any of the animals.
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