The victims were among 95 people, who appeared to be mostly from Afghanistan, Indonesia and Middle Eastern countries, pulled from the water Sunday after waves caused the boat to roll, Melbourne's The Age reported.
Among the asylum-seekers were 17 juveniles, including the 4- or 5-year-old boy who died, officials said.
Another young boy and a pregnant woman were injured and received medical treatment aboard a customs rescue boat.
Home Affairs Minister Jason Clare said the boat capsized at approximately 11 a.m. local time after two customs officers boarded the vessel, which had issued a distress signal for an unknown reason.
The officers also had to be rescued from the water approximately 16 miles from Christmas Island, The Age reported.
"We are confident that we have recovered all that we saw in the water," said Rear Adm. David Johnston, head of the Border Protection Command.
Barges ferried the asylum-seekers to shore.