The move came after US President Barack Obama blamed a Yemen-based al-Qa'ida affiliate for the foiled Christmas Day attack on a US airliner, and a day after a visit by the American regional military commander, General David Petraeus.
Al-Qa'ida's franchise in Yemen had called on Monday for embassies to be targeted as it claimed responsibility for the thwarted attack on the Detroit-bound Northwest airliner.
“The US Embassy in Sanaa is closed today, January 3, 2010, in response to ongoing threats by Al-Qa'ida in the Arabian Peninsula (AQAP) to attack American interests in Yemen,” said a statement posted on the embassy's website.
On Thursday the US mission sent a warden message to American citizens in the country reminding them of the “continuing threat of terrorist actions and violence against American citizens and interests throughout the world”.
AQAP on Monday urged further attacks on Westerners in the Arabian Peninsula.
“We call upon every Muslim who cares about his religion and doctrine to assist in expelling the apostasies from the Arabian Peninsula, by killing every crusader who works at their embassies or other places, declare it an all-out war against every crusader on Mohammad's peninsula on land, air and sea,” an AQAP statement said.
Both London and Washington have agreed to fund Yemen's special Counter-Terrorism Unit after Mr Obama on Saturday for the first time singled out the al-Qa'ida franchise in Yemen for the thwarted attack.
The special force had in the past received US training and assistance.
On September 17, 2008, the US embassy was the target of an attack claimed by al-Qa'ida in which 19 people were killed - seven attackers and 12 others, including Yemeni guards and civilians, one of them an American woman.
Last month the defence ministry newspaper said that a raid north of the capital on December 17 killed four suspects and foiled a plot to bomb the British embassy in Sanaa.
Yemen yesterday welcomed the British and US decision to fund the special force.
“Any assistance provided to Yemen's counter-terrorism force will be most welcome,” a government official said.
The official also said that Sanaa would need help to modernise its coastguard “in light of the danger coming from Somalia”.
Somalia's Shebab insurgents pledged on Friday to send militants across the Gulf of Aden to Yemen to help the al-Qa'ida affiliate behind the failed US airliner bombing.
Mr Obama on Saturday blamed Al-Qaeda's Yemen branch for the attack on the US jet by 23-year-old Nigerian suspect Umar Farouk Abdulmutallab.
“We know that he travelled to Yemen, a country grappling with crushing poverty and deadly insurgencies,” Mr Obama said in an address posted on the White House website.
“It appears that he joined an affiliate of al-Qa'ida, and that this group, al-Qa'ida in the Arabian Peninsula, trained him, equipped him with those explosives and directed him to attack that plane headed for America.”
General Petraeus on Saturday personally delivered a message from Mr Obama to Yemeni President Ali Abdullah Saleh on bilateral cooperation against terror groups.
Britain, meanwhile, has called an international meeting on combating extremism in Yemen for London on January 28, in parallel with a conference on Afghanistan drawing senior ministers or leaders from more than 40 nations.
Yemen is the ancestral homeland of al-Qa'ida chief Osama bin Laden.