The vessel was carrying 32 people, including members of the Rohingya Muslim minority from Myanmar, Iranians and a Bangladeshi, who wanted to reach the Australian territory of Christmas Island, police said.
But the small, wooden vessel sank off West Java province early yesterday after being battered by big waves, provincial police spokesman Martinus Sitompul told AFP.
The Australian Immigration Minister Scott Morrison has said the sinking highlighted the dangers of people-smuggling as hundreds of asylum seekers have died trying to make the sea voyage to Australia in recent years.
The Bangladeshi asylum seeker and two from Myanmar including a two-year-old toddler drowned but the other 29 were rescued by the fishermen and handed over to immigration authorities, he said.
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"This further loss of life is as tragic as all those that preceded it in similar circumstances, and we extend sympathies to the families of those affected," Morrison said.
"It is especially tragic as these deaths were needless and avoidable."
"This latest incident highlights once again the fatal consequences of people-smuggling, particularly in this most dangerous time of the year," he said, referring to the annual monsoon season.
Asylum-seeker boat arrivals have dropped dramatically under the new conservative government of Prime Minister Tony Abbott, which has retained the policy of the former administration of sending all boatpeople to Papua New Guinea or Nauru for permanent resettlement.
But there has been a recent spike, with close to 200 people arriving on four boats in the week up to December 6.