"It should be clear to the Russian side that such actions won't add legitimacy to these puppet regimes," Alexander Nalbandov, the Georgian deputy foreign minister said on Thursday.
Venezuela is the third country to recognise the two regions as independent, after Russia and Nicaragua.
Moscow announced its decision to recognise the regions in August last year, after crushing a Georgian attempt to retake the breakaway province of South Ossetia.
But Russia's allies in the former Soviet Union have so far resisted pressure to follow suit, fearful of setting precedents that could threaten their own sovereignty.
Georgia, backed by the European Union and the US, has condemned the Russian-sponsored moves as illegal and has called for its full territorial integrity to be respected.
Medvedev, who thanked Chavez for his decision, later said he was willing to sell tanks and other weapons to Venezuela after talks in Moscow, Russia's capital.
"We will supply Venezuela the weapons that Venezuela asks for. In accordance with all international law, of course," he said.
But he did not elaborate on whether a specific arms deal had been made, saying "these sorts of contracts are never signed in public".
Chavez said Venezuela was building up its military with Moscow's help, but insisted that this was not directed against any
"We have signed deals with the Russian government. However, these deals are not directed at anyone," he said.
In recent years Venezuela has signed over $4bn worth of arms contracts with Russia, and last November its navy held joint exercises with Russian warships in the Caribbean, traditionally seen as a US domain.