Sean McCormack, a state department spokesman, identified the woman as Susan el-Baneh, saying she was killed while standing in line with two members of her family who were applying for visas to visit the United States.
The suicide bomber drove a car close to the embassy early on Wednesday before detonating his explosives, leaving part of the building on fire, witnesses said.
Armed men, some reportedly dressed in army uniforms, then attacked the embassy from a second car.
The interior ministry said that six guards, four civilians and six attackers died in the assault.
Islamic Jihad in Yemen also on Wednesday threatened to target the British, Emirati and Saudi Arabian embassies in the country.
'War with extremists'
George Bush, the US president, said the attack was a bid by "extremists" to drive the US out of regions like the Middle East.
"This attack is a reminder that we are at war with extremists who would murder innocent people to achieve their ideological objectives," Bush said as he met General David Petraeus, the former senior US commander in Iraq.
"One objective of these extremists as they kill is to try to cause the United States to lose our nerve and to withdraw from regions of the world, and our message is - is that we want to help governments survive the extremists, we want people to live normal lives," Bush said.
The US embassy has been attacked four times since 2003, most recently in March when a volley of mortars, apparently targeting the compound, hit a neighbouring girls high school instead, killing a Yemeni guard and wounding dozens of girls.
A residential compound used by US oil workers in Sanaa had also come under attack from rockets at that time.
The embassy called on Americans in Yemen to "exercise caution and take prudent security measures, including maintaining a high level of vigilance, avoiding crowds and demonstrations, keeping a low profile, varying times and routes for all travel".
There have been several attacks by fighters in Yemen in recent years.