Georgia's interior ministry says the suspects, which include Georgian military officers, had been providing secret information about the country's military to Russia.
The alleged undercover agents are accused of passing on information about weapons, military communications and coordination with foreign armies.
Georgia says the ring was smashed in an undercover operation that saw a former Soviet army officer working as a double agent for Georgia. The spy was able to obtain computer hardware and software, which allowed Tbilisi to decipher encryption codes belonging the Russians.
Russia immediately denounced the arrests, which were announced on the annual day Russia celebrates its military intelligence service.
Diplomatic relations between Georgia and Russia are mostly frozen after the neighbours fought a brief war in 2008. These arrests are unlikely to improve relations between the two.