The state security service said the two were attempting to sell 40 grams (1.4 ounces) of uranium-238 isotope for $2.8 million (2.4 million euros).
The suspects were arrested in the Black Sea resort of Kobuleti, investigator Savle Motiashvili told journalists.
If convicted, they could face of up to 10 years in prison.
While radioactive uranium-238 is not suitable for a nuclear weapon, it can be used to make a dirty bomb, a conventional explosive that contains radioactive material.
The latest arrest highlighted concerns that extremists can get hold of unsecured radioactive materials in the former Soviet Union.
Over the past decade, Georgia and neighbouring Armenia have reported numerous cases of their nationals trying to sell radioactive substances.
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