 Mr Zhvania played a prominent role in the Rose Revolution
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Georgian President Mikhail Saakashvili has said he is taking charge of the government following the death of his prime minister on Thursday.
Zurab Zhvania, 41, was found dead in an apartment in Tbilisi, apparently poisoned by gas from a faulty heater.
Officials say security guards found his body after breaking into a flat owned by friends early on Thursday.
Mr Saakashvili told a crowd in Tbilisi that he was "taking responsibility for leading the executive".
"I am ordering the government to return to work," he added.
Mr Zhvania was once an ally of the previous President, Eduard Shevardnadze.
But he turned against him and played a prominent role in the 2003 Rose Revolution that ousted Mr Shevardnadze.
Interior Minister Vano Merabishvili said Mr Zhvania had arrived at the flat at about midnight local time on Wednesday (2100 GMT).
Security guards became suspicious after the prime minister failed to answer his phone for several hours.
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 Georgia will stand firm, and I hope I will stand firm because it is firmness that we need the most at present
Mikhail Saakashvili,
Georgian President
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They broke in around 0400 to find Mr Zhvania dead in an armchair.
The body of his friend and the owner of the flat, named as Kremo-Kartli region deputy governor Raul Usupov, was found in the kitchen.
No foul play was suspected, Mr Merabishvili said, but the body had been taken to the coroner's office for further examination.
David Morchiladze, the general director of Tbilgaz - the company supplying gas to Tbilisi - said there was an Iranian-made heater installed in the flat which broke safety regulations.
"Carbon monoxide was bound to be collected in the flat," he said. His deputy added that the flat, which Mr Usupov had moved into only a few weeks ago, had no vent for the gas.
'Great patriot'
Georgian President Mikhail Saakashvili held an emergency government meeting which was shown live on Georgian television.
"Georgia has lost a great patriot whose entire life was devoted to tireless and selfless service to our country. I have lost my closest friend, most trusted adviser and greatest ally," Mr Saakashvili said, addressing his ministers.
"I hope you will stand firm, Georgia will stand firm, and I hope I will stand firm because it is firmness that we need the most at present."
Mr Saakashvili said that his thoughts were with "Zurab's wife Nino, his mother Irma and his three most beautiful children".
Another Rose Revolution leader, parliamentary speaker Nino Burjanadze, cut short her visit to Italy and is returning to Georgia.