The building, located in the Lidingö suburb, houses the Russian trade mission in Sweden and was seized by Swedish authorities in accordance with an international arbitration at the Stockholm Chamber of Commerce.
The chamber had ruled that Russia needed to compensate German businessman Franz Sedelmayer for the nationalization of his company in Russia in 1992.
Sedelmayer won every appeal up to the Supreme Court, which issued its final sentence in 2011, to the dismay of Moscow.
On Tuesday, the Swedish government agency for debt collection, Kronofogden, announced on its website the sale of the 2,800-square-metre building for €2.3 million ($3.2 million)
Russia claims that Swedish justice has violated diplomatic immunity.
"The Russian party does not recognize these acts of bailiffs ... nor the judicial decision itself, which the Russian Federation sees as a gross violation of international law," the Russian Foreign Ministry said in a statement.
Viktor Khrekov, spokesman for the Office for Presidential Affairs warned that the Russian diplomats planned to stay in the building.
"Any attempt to enter illegally... will be immediately prevented," Khrekov told Russian newswire Interfax.
The buyer is a Swedish investor, Billy Uney, who said he was willing to rent the building to Russia.
"If they want to stay, they'll have to pay like anybody else," he told Swedish daily Svenska Dagbladet (SvD).
Sedelmayer said he was very pleased with the final sum.
"We couldn't have got more," he told the same newspaper.
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