Zhvania was at a friend's house when the accident occurred, Interior Minister Vano Merabishvili said in a live broadcast on Rustavi-2 television on Thursday.
Security guards broke through a window early on Thursday when they heard no sign of life inside the home several hours after the prime minister arrived, Merabishvili said.
Zhvania had entered the home at about midnight (2000 GMT) on Wednesday, and the guards entered the apartment between 4am and 4.30am.
His host Raul Usupov, deputy governor of Georgia's Kremo-Kartli region, was also killed. "It is an accident," Merabishvili said. "We can say that poisoning by gas took place."
An Iranian-made, natural gas-powered heating stove was in the main room of the house, where a table was set up with a backgammon set lying open upon it.
"It is an accident"
Georgian interior minister
Zhvania was in an armchair; Usupov's body was found in the kitchen.
"It all happened suddenly," Merabishvili said.
Central heating is scarce in Georgia, and many people use gas or wood stoves in their homes.
A long-time politician, the 41-year-old Zhvania was part of the opposition to former Georgian president Eduard Shevardnadze and played a prominent role in protests that led to his ouster after allegedly fraudulent elections in November 2003.
President Mikhail Saakashvili, who led the protests, named the moderate Zhvania prime minister following his landslide election victory in January 2004.