The men were arrested in the ex-Soviet republic's second-largest city of Kutaisi as they attempted to sell a container of americium-241 for 300,000 euros ($359,400), Georgia's state security service said in a statement.
They face up to 10 years behind bars.
Americium-241 is the most prevalent isotope of americium in nuclear waste and is commonly found in smoke detectors.
It is produced when plutonium absorbs neutrons in nuclear reactors or during nuclear weapons tests, according to the US Environmental Protection Agency.
Extremely toxic and radioactive, the isotope poses a health risk when ingested or inhaled.
Concerns have grown over the past decade that extremists can get hold of unsecured radioactive materials in the former Soviet Union.
Georgia and neighbouring Armenia have reported numerous cases of their nationals attempting to sell radioactive substances.
Since 2003, Georgia has foiled several attempts to smuggle weapons-grade uranium.
In March 2019, its security services stopped two men in the Black Sea resort of Kobuleti from trying to sell radioactive uranium for $2.8 million.
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