Britain said it believed there was a heightened threat of "terrorist attacks" in the Kenyan capital Nairobi and that attacks "may be in the final stages of planning".
The Foreign Office also revealed that British counter-terror police travelled to Kenya last month to assist the authorities following the arrest of a British national in the main port of Mombasa.
"The Kenyan authorities have alerted the public to a heightened threat from terrorist attacks in Nairobi. We believe that terrorists may be in the final stages of planning attacks," a Foreign Office statement said.
It said attacks could be "indiscriminate" and target "Kenyan institutions as well as places where expatriates and foreign travellers gather, such as hotels, shopping centres and beaches".
"We strongly advise British nationals to exercise extra vigilance and caution in public places and at public events," the statement added.
The Foreign Office did not identify a group behind the possible attacks, but Kenyan forces are currently fighting Al-Qaeda-linked Shebab insurgents in southern Somalia.
Kenya sent troops across the border into Somalia in October to battle the hardline militants it blames for a spate of attacks on home soil, and are fighting alongside Somali pro-government forces.
The Foreign Office said later that a Briton had been arrested in Mombasa and officers from the counter-terror unit of London's Metropolitan Police were working with Kenyan authorities.
"British counter-terrorism authorities are working closely with Kenyan authorities on the case of a British national arrested on 19 December in Mombasa," said a spokeswoman.
"A team from the UK's Met Police CT team SO15 deployed to Kenya in late December to assist the Kenyan authorities with their investigation. They have now returned.
"We have also provided consular assistance to the British national."
