Superintendent Ajith Rohana said Australia's coastguard intercepted the trawler carrying the Sri Lankans near the Indonesian coast, before handing the asylum-seekers over to Sri Lanka's navy on Thursday.
"The boat left Sri Lanka on November 1," Rohana said, adding that six children were among the passengers.
"Investigations are being conducted by the anti-people smuggling unit of the CID (Criminal Investigation Department)," Rohana said.
"They are being held in custody, but will be taken before a magistrate shortly."
The returns were the first since July when a boat loaded with 41 nationals was intercepted by Australia.
Sri Lanka charged them with illegally leaving the country, and their cases are due to be taken up by a court next May.
Australia has gifted two vessels to Sri Lanka's navy to patrol its shores and stop boats leaving the island, as part of Canberra's hardline border protection policy.
Prime Minister Tony Abbott has vowed to stop asylum-seekers arriving on rickety boats following dangerous voyages.
Applications for asylum rejected
A statement by Immigration Minister Scott Morrison has confirmed the vessell was handed over to Sri Lankan authorities.
One of the group of 38 asylum seekers will be taken to an Australian offshore immigration detention centre.
'The suspected illegal entry vessel (SIEV) was intercepted by Border Protection Command (BPC) North-West of Cocos (Keeling) Islands on 15 November 2014. All persons aboard the SIEV were safe and accounted for and at no stage was the vessel in distress,' the statement says.
'Thirty-seven Sri Lankan nationals were transferred at sea from a vessel assigned to BPC to Sri Lankan authorities on Wednesday evening, in mild sea conditions East-South-East of Galle.
'Consistent with Australia’s international obligations, all persons intercepted and returned were individually assessed under an enhanced screening process, as also practiced by the previous government. Interviews were conducted in person, on board the vessel assigned to BPC, by trained protection officers, supported by qualified Tamil and Sinhalese interpreters.'
'In one case a referral for a refugee determination process was recommended. In such cases, the Government's policy is to transfer these persons to either the country of Papua New Guinea or the country of Nauru for processing. The individual remains in the care of Australian Government authorities and will be transferred to an offshore processing centre.'
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