No one was injured in the blaze and all non-essential staff have been airlifted from the West Atlas rig, operators PTTEP said.
The fire, which started during an attempt to plug the leak, comes as environmental campaigners criticised PTTEP and the Australian government over their handling of the crisis.
An estimated 400 barrels of oil a day have escaped from the rig since Aug. 21.
Officials now plan to pour mud into the leak hoping to remove the source of fuel from the fire, which was sending huge plumes of smoke into the sky.
Jose Martins, PTTEP Australasia's chief financial officer, said the company didn't know how the blaze started.
"Presently there are many unanswered questions, including what caused the fire," Mr Martins said. "Our sole focus now is the safety of all personnel, bringing the fire under control and completing the well kill."
Martin Ferguson, the Federal Resources Minister, said that once the spill was contained he would launch an official inquiry.
"Our requirement is to assess the cause of the accident and any lessons to be learnt, and that could lead to a change in the regulatory environment," he told Australian Broadcasting Corp. radio.
He admitted that the accident, the first major incident in the past 25 years of offshore drilling, had "clearly had an impact on the standing of the oil and gas industry in Australia".
The oil slick from the rig, which is located about 150 miles off Australia's northwest coast, now stretches across thousands of miles of remote ocean. Indonesia said last week that thousands of dead fish and clumps of oil have been found drifting near its coastline.
Environmental groups have criticised the government's response to the spill, saying it was threatening bird and marine life off Western Australia's resource-rich northern coast.
Bob Brown, the leader of the Greens Party, called on Mr Ferguson to resign over his handling the emergency.
"This is an irresponsible minister who has made a bad situation worse. He should go.
"The whole thing is chaotic, It's a mess that's gone from bad to worse. We have to hope that today they will successfully plug now that they've actually found the well neck."