Georgian Security Minister Valery Khaburdzania said the rebels - several of whom were injured - were being interrogated.
The arrests come after a week of heightened tensions between Georgia and Russia, after Moscow said Chechen rebels hiding in Georgia's Pankisi Gorge infiltrated into its territory and killed eight borderguards.
Russia has also accused Georgia of providing a base for what it terms "international terrorists" and has not ruled out a military operation against the rebels.
At the same time, Georgia has accused Russia of sending combat aircraft to raid its territory, on the pretext of attacking Chechen rebels in the mountainous border region.
Georgia said the Russian attacks amounted to aggression against a neighbouring sovereign state.
Russia denied the allegations.
Russia unmoved
The tension is escalating just as US Army officers in Georgia prepare to train Georgian troops to fight international terrorism.
Georgia said it would not allow Russia to launch an operation on its territory.
Earlier, Mr Khaburdzania said that Georgia would grant an amnesty to some militants in the Pankisi Gorge, where nearly 4,000 Chechen refugees are believed to be hiding.
"Those people who give themselves up to the Georgian authorities unarmed will enjoy the same rights as other refugees," Mr Khaburdzania said.
Despite the arrests, Russia accused Georgia of failing to fight terrorism.
"As recent events have shown, international mercenaries feel at home in the Pankisi Gorge," Russian Foreign Minister Igor Ivanov told the Interfaks news agency.
"We are prepare to help in the fight against international terrorism which also threatens Georgia and may soon do so to a greater degree. But such choice must be made in Tbilisi."
The BBC's Caroline Wyatt in Moscow says if Russia carries out its threat to launch a military operation in Georgia, it could lead to a new war in an already unstable region.