The state security ministry said there were no casualties but the explosion was powerful.
Television correspondents at the scene said the blast affected part of the building housing radio studios, but the radio workers had gone home for the night. Television pictures showed broken windows and small kiosks near the building were also damaged.
Russia's ambassador to Georgia, Vladimir Chkhikvishvili, said the blast offered further proof that former Soviet Georgia, which is plagued by unemployment, corruption and poverty, had not settled down after the "velvet revolution".
"What has just happened is evidence of the unstable situation that is Georgia," he said.
Georgian president Eduard Shevardnadze quit after mass protests last month following a parliamentary election
criticised for being corrupt. The new leadership is holding new presidential elections on January 4.