Immigration Minister Scott Morrison said 27 people had been found living on a remote beach on the island after their boat sank Monday, the Australian Broadcasting Corp. reported.
The asylum seekers were found Thursday after security authorities saw several of them walking along a road.
One man was taken to hospital with minor injuries believed sustained while escaping from the sinking boat, the Australian broadcaster said.
Morrison said it was an "unusual incident" that the so-called suspected irregular entry vessel had landed without being detected.
"I can confirm [the asylum seekers] are in the care of the Department of Immigration and Border Protection at the Phosphate Hill transfer facility," he said.
"We should never forget that this is a very big ocean in that vicinity. These are very small vessels. These 27 people who are now safe should count themselves extremely fortunate that they did not suffer a far worse fate.
Since winning the general election in September Prime Minister Tony Abbott's Liberal government reorganized the country's 12 border and immigration agencies into one force under the banner Operation Sovereign Borders.
ABC reported Morrison conceded the failed surveillance during his weekly briefing on Operation Sovereign Borders.
He also said four asylum seeker boats had been intercepted in the past week and border agencies have in custody the ships' 162 asylum seekers and six crew.
The total doesn't include the 27 asylum seekers who made it to Christmas Island -- located about 1,600 miles from Australia's west coast -- but less than 200 miles from Indonesia.
The territory has one of Australia's main asylum seeker detention centers.
Australia also operates extra-territorial detention centers on Nauru, formerly the British colony of Pleasant Island, and Papua New Guinea under agreement with those governments.
Army Lt. Gen. Angus John Campbell, Commander of Operation Sovereign Borders, said people smugglers are taking advantage of good sailing conditions ahead of the monsoon season.
"We do have radar capability on both our vessels and at Christmas Island. But depending on the general weather conditions and the sea swell, the size of the craft, it is possible, but rare, to see these sorts of incidents arise," Campbell said
Campbell, formerly head of Australia's forces in Afghanistan, also said the cluster of recent arrivals could be the result of heightened people smugglig activity to fill their boats.
Successive Australian governments in the past decade have wrestled with rapidly increasing numbers of asylum seekers arriving in unseaworthy boats after paying smugglers in Asian countries for the often dangerous passage.
One the vessels was wrecked on rocks in high seas yards from the shore of Christmas Island, killing 50 people in December 2010. The disaster was filmed by media whose clips showed people jumping into the churning sea amid bodies floating in the water.
Government figures show more than 17,000 asylum seekers arrived by boat last year and by June this year the number was over 13,000.