"We can confirm the detention of a British national in Nairobi and we are making contact to offer standard consular assistance," she said on Wednesday, without saying if the suspect was a man or a woman.
The comments came as witnesses to the Kenyan shopping centre massacre have said a woman who spoke English was one of the attackers.
The developments come as British counter-terrorism officials try to establish if Britons were involved in the attack, and whether or not Samantha Lewthwaite, already wanted for terror offences in Kenya, commanded the killers.
Lewthwaite is the 'white widow' of Jermaine Lindsay, one of the 7/7 suicide bombers.
Meanwhile, Somalia's Shebab insurgents claimed Wednesday 137 hostages they had seized died in a Nairobi shopping mall siege, figures impossible to verify and higher than the number of people officially registered as missing.
The Al-Qaeda-linked fighters, in a message posted on Twitter, said "137 hostages who were being held by the mujahedeen" had died.
They also accused Kenyan troops of using "chemical agents" to end the four-day stand-off.
"In an act of sheer cowardice, beleaguered Kenyan forces deliberately fired projectiles containing chemical agents," one tweet read.
"To cover their crime, the Kenyan government carried out a demolition to the building, burying evidence and all hostages under the rubble."
President Uhuru Kenyatta announced an end to the 80-hour bloodbath late Tuesday, with the "immense" loss of 61 civilians and six members of the security forces.
Police said the death toll was provisional, with the Kenyan Red Cross listing 63 people as still missing.
There was no immediate response from Kenya's government, but the Shebab have in past made repeated outlandish claims, especially on their Twitter site.
The Shebab said they carried out the attack in retaliation for Kenya's two-year battle against the extremists' bases in the country.
In one of the worst attacks in Kenya's history, the militants marched into the four-story, part Israeli-owned mall at midday Saturday, spraying shoppers with automatic weapons fire and tossing grenades.
Kenya on Wednesday began three days of official mourning, with flags flying at half mast, while rescue workers scoured the wreckage of the mall for bodies.
Close to 200 were wounded in the four-day siege, which saw running battles between militants and security forces in the complex, Nairobi's largest shopping center and popular with wealthy Kenyans, diplomats, UN workers and other expatriates.
BA/BA