It quoted court papers which said he was accused of causing "disrepute to the country and the army by providing alleged videos to (Britain's) Channel 4 television" for its documentary "Sri Lanka's Killing Fields".
The paper said the questioning would be carried out by Sri Lanka's Criminal Investigations Department.
The British High Commission in Colombo said it had no immediate information on the case.
The Lakbima daily paper said police had sought the man's detention because he posed a "threat to national security".
Police spokesman Prishantha Jayakody declined to discuss the case, but confirmed a man was arrested in connection with "supporting terrorist activities".
The arrest came after the military said Wednesday it had original footage that exposed the "malicious intentions" behind the Channel 4 documentary.
Sri Lanka's military said its "unaltered" video suggested that what the documentary presented as Sri Lankan soldiers executing Tamil rebel prisoners were actually rebels clad in army fatigues.
In the audio track of the footage in the documentary, aired last month in Britain and later in Australia, the soldiers spoke in the language of Sri Lanka's Sinhala majority.
The military said the video that the military had analysed had a Tamil soundtrack, suggesting the killers were rebels.
Sri Lanka has persistently denied that its troops staged any war crimes while battling the Liberation Tigers of Tamil Eelam (LTTE), who were crushed in an offensive that ended in May 2009.Colombo has also accused Channel 4 and Western nations of waging a campaign to discredit Sri Lanka's human rights record by producing reports of alleged war crimes and crimes against humanity.