The government has acknowledged holding them and says most will be put through a process it calls “rehabilitation”.
The Sri Lankan army defeated separatist Tamil Tiger rebels after 26 years of bloody civil war in 2009.
Thirty-eight people, out of 150 initially questioned, are under arrest after being detained in the Trincomalee area of north-east Sri Lanka, police said.
Police spokesman Ajith Rohana told the BBC that the 38 had past links to the rebels and that their families had been informed.
The leader of the Tamil National Alliance (TNA), R Sampanthan, says relatives of the detainees have no idea where their husbands or sons are.
He told the BBC’s Charles Haviland in Colombo: “I hope they are safe. I hope they’re alive. But that is a matter which is in doubt, because the whereabouts of these persons are not known.”
The police spokesman said they were taken in under the Prevention of Terrorism Act on an order signed by President Mahinda Rajapaksa in his capacity as defence minister.
The spokesman said most of the detainees will be put through a year-long process known as rehabilitation, although those accused of serious offences would be tried.