The Federal Security Service gave the intelligence officer's surname as Kherksladze, and said the suspect had described himself as the deputy head of Georgia's Foreign Intelligence Service.
The FSB said Kherksladze has been running a network of agents in Russia collecting information, "including on military and strategic facilities in the Southern Federal District."
The FSB also said Georgian secret services had tried to organize underground militant groups in the North Caucasus.
The Russian secret service said that it had arrested a Russian national, one Ramzan Turkoshvili, who "confessed to being recruited by Georgian secret services with the direct involvement of one of the leaders of terrorists hiding in the Pankisi Gorge."
The FSB said that the intelligence officer had been given the task of "organizing militant resistance to federal authorities" in Ingushetia and other regions of Russia's Southern Federal District, adding that he was also believed to have been a link between militant groups in Russia and Georgian secret services.
The Russian Republic of Ingushetia borders on Chechnya and has been the scene of increasing militant attacks on police and federal forces of late.
FSB head Alexander Bortnikov said on Monday that the security service had detained 10 Georgian intelligence service officers who were spying on military facilities and preparing terrorist attacks, including in Russia.
Security was tightened on the Russian border following a major ground and air offensive by Georgia against its breakaway republic of South Ossetia on Friday. The attack prompted Russia to send in tanks and hundreds of troops and eventually expel Georgian troops from the province. Russia has said at least 1,600 civilians were killed by Georgian forces during the attack. A total of 34,000 people are also reported to have fled across the Russian border.
Russia has also beefed up its presence in Abkhazia, another secessionist Georgian republic.