It said the incident happened in Anaklia, near the de facto border with Abkhazia, where Russian coastguard ships patrol the area.
"The Kremlin employs such methods in order to escalate the situation in the territories adjacent to Georgia's occupied regions and provide all preconditions to push the conflict into a 'hot' stage," the Georgian foreign ministry said.
There was no immediate response from Russian authorities.
About 21 Georgian villagers were detained in South Ossetia last month and accused of illegally crossing the border to search for wood. They were all released.
The boundary line between South Ossetia and Georgia is poorly-defined and runs through agricultural land.
Tensions in the Black Sea ran high earlier this year when Georgia seized several cargo vessels accused of trading with Abkhazia without permission from Georgian authorities.
Russian forces have controlled the de facto borders of Abkhazia and South Ossetia since August last year, when Moscow crushed a Georgian assault on South Ossetia and subsequently recognised both territories as independent states.
Officials from Russia, Georgia and the two breakaway regions are meeting in Geneva on Wednesday for their latest round of internationally-mediated security discussions.