The 14,990-ton Uniceb, a Panamanian-registered vessel bound for Jordan from Western Australia, caught fire off Tanzania earlier this week.
A tug is on its way to salvage the ship, which is adrift, Australian Broadcasting Corporation radio reported on Friday. Other unconfirmed reports said the ship might have sunk.
Fifty-four crew were rescued by a passing freighter, but the stricken vessel's engineer was lost overboard. No crew remained on board.
Australia regularly exports live sheep to the Middle East where the animals are slaughtered according to Islamic halal requirements.
Hugh Wirth, president of the Royal Society for the Prevention of Cruelty to Animals, condemned live sheep exports as cruel. Details of the incident are sketchy. But Mr Wirth said there was no doubt that many sheep have already died in the flames. Others will die soon without food and water.
Mr Wirth alleged that mistreatment of sheep aboard specially modified export ships is common. Up to 8 per cent of the animals die in transit on successful voyages, he said, adding that "this wouldn't be the first time a complete cargo of live sheep has been lost to fire."
Although it admits there are problems, the Australian government said live sheep exports are worth 500m Australian dollars (pounds 253m) a year and will continue.
"Middle East countries want those exports live," a spokesman for Primary Industries Minister John Anderson said.
The Australian Meat and Livestock Corporation said all sheep ships leaving Australian ports must comply with strict animal welfare requirements.
The corporation's divisional manager Lloyd Beeby said the status of the Uniceb is unclear.
"It don't think anyone knows if it's afloat or sunk," he said.