The 41-strong group was brought ashore at the southern port of Galle, 115 kilometres south of the capital, and taken to the notorious high-security Boossa prison on Monday.
"They will be brought before the Galle magistrate on Tuesday," police spokesman Ajith Rohana told AFP.
Correcting an earlier report, he said the group comprised 28 men, including four from the minority ethnic Tamil community, four women and nine children.
"In respect of the children, we will take them also before the magistrate, but we won't press charges and we won't object to their being released," he added.
Leaving the country illegally is a criminal offence punishable with up to two years in jail.
"As soon as they were taken off the Samudra (Sri Lankan navy boat), the men were driven under high security to Boossa," a local police official told AFP, referring to the jail which earned notoriety for alleged torture from the early 1980s.
The Sri Lankan navy gave a different location for the transfer of the men from a boat belonging to the Australian Border Protection Command which had intercepted their vessel.
Australian Immigration Minister Scott Morrison in a statement said the transfer took place "just outside the port of Batticaloa", but there is no port in Batticaloa, which is 300 kilometres east of Colombo by road.
Sri Lanka's navy spokesman Kosala Warnakulasooriya said the 41 were taken into custody in "deep waters off the southeastern coast of Sri Lanka", but gave no further details.
The navy spokesman said they were unaware of the fate of 153 Sri Lankans in another boat who were reportedly intercepted by Australia last week after setting off from southern India in late June.
There were claims that Australia could be breaking international law by screening the would-be asylum-seekers at sea by teleconference and returning them involuntarily to a country in which they had a fear of persecution.
Lawyers arguing that the mid-sea transfers are illegal succeeded on Monday in obtaining a temporary order from an Australian court barring the handover of the 153.
Morrison is due in Sri Lanka on Wednesday to meet top officials, and will also take part in a ceremony to hand over the second of two patrol boats donated to Sri Lanka last year.
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