Russia, which has watched with unease its southern neighbour's aspirations to join the EU and Nato, handed Georgia's ambassador in Moscow a strongly worded protest note telling Tbilisi to free the detained officers.
Vano Merabishvili, the Georgian interior minister, said: "A few hours ago our counter-intelligence detained four GRU [Russian army intelligence] officers and more than 10 Georgian citizens.
"We had information that this group had been planning a serious provocation.
"Another Russian officer is now hiding at the headquarters of Russian troops in the Transcausus, this is why the building is cordoned off by Georgian police."
He said the detained Russians and the Georgian citizens they had recruited had been collecting information on Tbilisi's relations with Nato, as well on its sea port and railway infrastructure, opposition parties and army.
Merabishvili said: "Today we neutralised a very serious and dangerous group."
Reuters reporters saw about 100 unarmed policemen and security guards surrounding the regional Russian army headquarters - a compound near the Georgian capital's centre guarded by Russian soldiers with submachine guns.
Irakly Okruashvili, the Georgian defence minister, said the building would be blocked as long "as it hosts the persons charged with well-grounded accusations of espionage, subversive acts and other crimes".
He told Georgia's independent Rustavi-2 television: "Until now Russia's authorities have thought they are dealing not with the Georgian state but with Georgian territory without borders and state structures.
"But we have just shown that this is not so, and we won't allow this rampage of spies and agents to go on."
Russia's foreign ministry said the detention of the Russian officers was "an outrageous escapade proving the general anti-Russian policy of Georgia's leadership".
Yuri Baluyevsky, chief of Russian army staff, was quoted by Russian news agencies as saying: "This [detention] is sheer lawlessness by Okruashvili and his entourage."
The crisis follows months of tension between the two states.