"Ansar al-Sharia have targeted the US embassy in Sanaa with a (shoulder-launched) LAW rocket," the jihadist group posted on Twitter.
The attack came "in revenge for Muslim children targeted by a US drone when it bombed in Jawf province yesterday," the statement said.
Al-Qaeda in the Arabian Peninsula has been linked to a number of failed terror plots against the United States. Washington operates drones over Yemen, but US officials rarely acknowledge the covert programme.
Earlier, the mission said on Twitter that it had "no reason to believe the US Embassy was target" of the attack.
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It said the chancery was "unaffected" and that Yemeni authorities were investigating.
The attack comes a week after Shiite Huthi rebels swept across the capital taking control of key state institutions and becoming largely the only visible armed force in the streets of Sanaa.
On Thursday, Washington ordered a cut in its government staff in Yemen due to the "unpredictable" security situation, while an updated travel advice urged US citizens in the country to leave.