He had demanded around €2 million, a helicopter to leave the country and a Russian flag, Georgian media report.
Police in Georgia said 12 people who were held hostage in a bank by a gunman for hours on Tuesday have been freed.
The man -- who has not been identified -- had demanded around €2 million, a helicopter to leave the country and a Russian flag.
His demand was made via a video post on one of the hostages' Facebook pages.
It was not immediately clear whether anyone was injured in a standoff at a branch of the Bank of Georgia in Kutaisi, 180 kilometres northeast of the capital, Tbilisi.
Interior Ministry spokeswoman Ketevan Kovziashvili confirmed on Tuesday evening that the hostage-taker has been arrested.
Georgian police have opened a probe on multiple charges, including terrorism.