"Public services at the British Embassy in Cairo are suspended on Sunday," the embassy said on its website.
"The office of the British Consulate-General in Alexandria is operating as normal," it said. "Please do not come to the embassy building," the embassy advised.
The embassy declined to give details due to the sensitive nature of the matter but said it was working with Egyptian authorities to reopen as soon as possible.
"The decision to suspend public services at the embassy has been taken for security reasons and is in the best interests of our staff," the spokesperson said. "The decision is independent of our wider travel advice for Egypt."
One security source told Reuters it was not yet clear what threats had prompted the embassy to close its doors.
But another source, who spoke on condition of anonymity, said a suspected militant who was recently detained by Egyptian authorities had confessed to plans to target foreign embassies.
The British Foreign Office already advises against all travel to the volatile area of northern Sinai and all but essential travel to most of southern Sinai and to the west of Egypt, particularly near the border with Libya.
"There is considered to be a heightened threat of terrorist attacks globally against UK interests and British nationals from groups or individuals motivated by the conflict in Iraq and Syria. You should be vigilant at this time," the Foreign Office says on its Egyptian travel advice page.
"In light of the heightened tensions and recent attacks on Westerners in the region, the U.S. Embassy has recommended that its staff carefully scrutinize their personal movements and consider staying close to their residences and neighbourhoods over the coming period," it said in the message on its website.