He said that the peacekeepers, who are deployed in the breakaway region and a swathe of Georgian territory outside it, had detained two cars in the Georgian village of Ditsa.
Kulakhmetov said: "There were four people, apparently ethnic Georgians, in the car. Light firearms and two grenades were also found.
"The cars and the detained people were escorted to Tskhinvali. During the search of one of the cars, an explosive device equivalent to some 20kg went off."
The breakaway region's press department said the blast had damaged the headquarters and broken the windows of neighbouring buildings.
Thick black smoke plumed into the air after the explosion as police cars and ambulances rushed to the scene.
Eduard Kokoity, South Ossetia's leader, was quick to blame Georgian security services for the blast, Russia's Itar-Tass news agency said.
A Russian foreign ministry source, also seemingly pointing the finger at Georgia, layed the blame on unspecified forces "seeking to destabilise the situation".
Matthew Collin, Al Jazeera's correspondent in Tbilisi, the Georgian capital, said: "This is highly unusual ... and quite an ominous development."
Collin said that Georgian officials had told him that the explosion could only have been organised by Russian special services.
Russia has deployed peacekeepers at the base since the early 1990s.
Moscow says confiscating illegal weapons and explosives are part of the work carried out by its troops.
European Union monitors are currently in a Russian-controlled buffer zone around South Ossetia to begin a peacekeeping operation there.