They were arrested last week at a hotel near the Iranian border during a counter-terrorism raid, the newspaper reported.
The Times said it was the first time UK forces had detained British nationals in Afghanistan. The suspects were now being held in Helmand province, it added.
“The operation last week was believed to have been carried out in response to a suspected threat to British rather than Afghan security,” the paper said.
In London, both the Foreign Office and the Ministry of Defense confirmed the arrests but gave no further details.
“We can confirm that two British nationals have been detained in Afghanistan. Embassy staff are providing assistance,” the Foreign Office said.
The defense ministry added in a separate statement: “We can confirm that British Forces have detained two individuals in Afghanistan who claim to be British nationals.
“We are not prepared to comment further at this stage.”
Under NATO guidelines, most individuals detained by allied forces are released or transferred to the Afghan Authorities within 96 hours.
Britain has a national policy of detaining people longer than 96 hours in exceptional circumstances, particularly when authorities think they can get information to protect their forces or the Afghan population.
The Times gave no details of the nature of any threat posed to Britain by the pair.
It reported they were arrested in a covert mission involving British and Afghan forces while they were staying at the International Trade Center hotel in the western city of Herat.
On Wednesday, British troops handed responsibility for security in the capital of Helmand Province to Afghan forces as part of a planned pull-out of combat forces by the end of 2014.
