Australia's home affairs ministry said the number of dead and injured had yet to be confirmed.
"Border protection agencies have reported there has been an explosion or serious fire on board this vessel," Bob Debus, Australia's home affairs minister, said in a statement.
"There are reports from personnel on the scene that this incident has resulted in fatalities, serious injuries and that a number of occupants of the vessel are missing."
He said two navy patrol boats were providing assistance following the incident.
"The government's first priority is to address the immediate situation and to ensure the safety of life at sea."
An Australian state official said the asylum seekers had deliberately doused their own boat in petrol before the explosion, as the vessel drifted under the watch of the Australian navy.
"It is understood that the refugees on the boat spread petrol and that ignited causing the explosion," Colin Barnett, the Western Australian premier, said in Perth.
Barnett's claim could not be confirmed, and the government immediately responded by saying it was too early to speculate on the cause of the explosion.
Rear Admiral Alan Du Toit, of the Royal Australian Navy, said investigations will be carried out to determine the exact cause of the explosion.
"I really can't speculate on the cause," he said in Canberra. "Clearly this will be subject to appropriate inquiries by the appropriate authorities."
He said several navy sailors were also on board when the explosion happened, along with the crew believed to be Indonesian fishermen.
Thirteen boats carrying asylum-seekers have been discovered in Australian waters since the government of Kevin Rudd, the Australian prime minister, introduced policies last July that softened the country's treatment of asylum-seekers.
Refugees landing on Australian soil peaked in 2001 when more than 1,200 people arrived, mostly from the Middle East.
Many of these maritime journeys have been organised by professional people-smuggling rings.