Alexander Vinnik, who headed BTC-e, an exchange he operated for the cyber currency, was indicted by a US court in July on 21 charges ranging from identity theft and facilitating drug trafficking to money laundering.
Vinnik said he would appeal the extradition decision of the Thessaloniki court on Wednesday.
"We consider that the verdict is unjust and violates the norms of international law," the Russian foreign ministry said in a statement.
"Greek authorities received a request from the Russian attorney general that Vinnik be extradited to Russia" which "should have priority, as Vinnik is a Russian citizen," the ministry said.
The final decision on whether to extradite Vinnik will be made by the Greek justice minister.
The Russian has been languishing in a Greek jail since his arrest on July 25 in the tourist resort of Halkidiki, near Thessaloniki.
According to US authorities, Vinnik "stole identities, facilitated drug trafficking, and helped to launder criminal proceeds from syndicates around the world".
BTC-e, founded in 2011, became one of the world's largest and most widely used digital currency exchanges, but according to the US indictment, it was "heavily reliant on criminals".
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