No one was hurt in the blasts, which a reporter heard from the center of Tskhinvali.
Gunfire is an almost daily occurrence on the de facto border, which at its closest point runs just a few hundred meters from the southern edge of Tskhinvali.
Analysts warn of the risk of skirmishes boiling over into renewed hostilities in pro-Western Georgia, with tensions simmering ahead of next week's anniversary of the war.
The South Ossetian Interior Ministry said in a statement that two mortar rounds were fired towards residential buildings from the village of Zemo Nikozi, where Georgian police stand behind high sandbag walls ringing the village cemetery.
The Georgian Interior Ministry said the shooting came from Russian-backed South Ossetian forces in Tskhinvali, in the direction of Zemo Nikozi.
"It started with machine guns and then from large-caliber weapons, mortars," said ministry spokesman Shota Utiashvili. "We did not return fire."
Russia crushed a Georgian assault on Tskhinvali in August after weeks of escalating skirmishes, sweeping tanks and troops into Georgia proper to within 40 kilometers of Tbilisi.
Like the rebel Black Sea region of Abkhazia, South Ossetia threw off Georgian rule in wars in the early 1990s.
The West, nerves rattled over energy transit routes running through the South Caucasus, accused Russia of a "disproportionate response." The European Union brokered a ceasefire, and deployed 240 unarmed monitors.
An EU spokesman said the monitors were checking reports of shooting overnight, and were seeking contact with Russian forces through a hot line established to help diffuse clashes.
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