The embassy declined to give more details due to the sensitive nature of the matter but said it was working with the Egyptian authorities to reopen and resume full service 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."
It was not clear when the embassy would reopen. The British embassy website said the office of the British Consulate-General in Alexandria was operating as normal.
Insurgent attacks have mostly targeted Egyptian police and soldiers, killing hundreds in the past year, but Egypt's most dangerous militant group said on Monday it was behind the killing of an American oil engineer in the western desert in August.
Smaller bombs also regularly explode in Cairo and the Nile Delta, usually causing limited injuries.
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.
However, it released a statement on Dec. 4 warning staff not to stray too far from their homes.
"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.
It also urged U.S. citizens to remain alert.
(Reporting by Lin Noueihed; Editing by Mark Potter and Stephen Powell)