The U.S. State Department said it had no indication that the embassy was the target of the attack and that none of its staff were wounded.
The rocket landed 200 metres from the heavily fortified embassy, hitting members of the Yemeni special police force who guard the site. At least two were wounded, police said.
The attacker fired the rocket from a car using a M72 light anti-tank weapon before speeding away, a police source told Reuters.
Several hours after the attack, Ansar al-Sharia, an affiliate of al Qaeda in the Arabian Peninsula (AQAP), said on its Twitter account it had targeted the embassy with a rocket, injuring several guards and damaging a vehicle.
The group said the attack was revenge for a drone strike on Friday that had seriously wounded children in the northern al Jawf province.
Tribal sources confirmed that a drone strike killed two al Qaeda members and wounded two more in al Jawf on Friday, and that there were reports of some children having been wounded.
The United States regularly uses drones to attack Islamist militants in countries such as Yemen as part of a strategy to combat al Qaeda militants without committing troops on the ground.
Washington acknowledges using drones in Yemen but does not comment publicly on the practice. Al Qaeda and its affiliates in Yemen are among the most active wings of the network founded by Osama bin Laden.
Sanaa is already in turmoil after Shi’ite Muslim rebels seized control of much of the capital last week, hours before the accord was signed with other political parties providing for the creation of a new government.
Earlier on Saturday, Houthi rebels attacked the home of Yemen’s intelligence chief in Sanaa, in a sign of the fragility the power-sharing accord.
The takeover of the capital has given the Houthis unprecedented political power in Yemen, a U.S.-allied country whose political, tribal and sectarian unrest poses risks to the world’s top oil exporter Saudi Arabia next door.
President Abd-Rabbu Mansour Hadi has said Yemen may be heading for civil war.
The attempted attack on the embassy comes a day after the United States told its citizens to leave Yemen and said it was reducing the number of U.S. government staff there due to political unrest and fears of a possible military escalation.
The U.S. embassy has been the target of several attacks in recent years, including one in 2008 by al Qaeda affiliated militants in which 18 died.
In 2012, demonstrators angry at U.S.-made film they considered blasphemous attempted to storm the compound and in May this year, the embassy said armed individuals had attempted to kidnap two of its officers at a small commercial business in Sanaa. (Reuters)