So far, 110 people have been rescued from the vessel which was believed to be carrying around 200 asylum-seekers, with authorities saying: "We're still in that critical window where more lives could be saved."
"We have 110 survivors and three confirmed dead so far," a spokeswoman from Australia's Maritime Safety Authority (AMSA), which is working with Indonesia's search and rescue authority Basarnas, told AFP.
They were taken by ship to Christmas Island, a remote Australian territory in the Indian Ocean where they were given medical checks.
"They were rescued wearing life jackets and we are quite confident we will recover more survivors," added the spokeswoman, who said the water temperature was warm.
The ship, en route from Sri Lanka, issued a distress call and capsized 120 nautical miles north of Christmas Island, 2,600 kilometres (1,600 miles) from the Australian mainland on Thursday afternoon.
Christmas Island administrator Steve Clay told ABC radio that three of the survivors were admitted to hospital on their arrival, but the rest were OK.
"They were transferred to the jetty, put into buses and transferred up to the Phosphate Hill immigration facility," he said.
"They're getting medical checks up there. They appear calm and they were just sitting quietly."
The capsize is the latest in a series of refugee boat disasters in the Indian Ocean in recent years, as rickety, overloaded vessels packed with desperate migrants sink on their way to Australia.
Four merchant vessels, two Australian Defence Force ships and five aircraft are involved in the search.
"We're still in that critical window where more lives could be saved," said Home Affairs Minister Jason Clare.
"People can survive out there for up to 36 hours if they have either lifejackets or they have debris to hold onto."
Clare said about 40 survivors were found clinging to the upturned hull of the boat on Thursday afternoon, while others were discovered holding onto debris up to three nautical miles from the scene.
Though they come in relatively small numbers by global standards, asylum seekers are a sensitive political issue in Australia, dominating 2010 elections due to a record 6,555 arrivals.
Direct asylum-seeker journeys from Sri Lanka have historically been rare but navy sources in Colombo have reported a marked increase in Australia-bound people-smuggling operations.
Indonesia is a more common transit point for those trying to reach Christmas Island, which is closer to Java than mainland Australia, but many fail to reach their destination.
The UN's refugee agency said it was "deeply concerned" by the incident.
"This accident again underscores the dangerous nature of these hazardous journeys, and the desperate and dangerous measures people will resort to when they are fleeing persecution in their home countries," it said in a statement.
In December, a boat carrying around 250 mostly Afghan and Iranian asylum-seekers sank in Indonesian waters on its way to Christmas Island, with only 47 surviving.
Some 50 refugees were killed in a horror shipwreck on the island's cliffs in December 2010. Fifteen were children aged 10 years or younger.
The worst known refugee boat disaster off Australia in recent years was the sinking of the SIEV X in 2001, which killed 353 of the more than 400 asylum-seekers on board.