In a message on Twitter, Al-Qaeda's media branch said its fighters set off the explosive devices at an entrance to the embassy on Thursday night, according to SITE Intelligence Group.
There has been no announcement by US authorities of any attack, and American officials could not immediately be reached for comment on the claim, as AFP reports.
The announcement comes three weeks after Al-Qaeda said it had tried to assassinate US Ambassador Matthew Tueller with two bombs that were discovered minutes before they were to explode.
The devices had been planted outside the house of Yemeni President Abdrabuh Mansur Hadi and had been intended to explode when Tueller left after a visit there on September 8, Al-Qaeda said.
Yemen is a key US ally in the fight against Al-Qaeda, allowing Washington to conduct a longstanding controversial drone war against the group on its territory.
The United States considers Al-Qaeda in the Arabian Peninsula to be the most dangerous arm of the terrorist organisation.
AQAP was born out of a 2009 merger of its franchises in Al-Qaeda founder Osama bin Laden's native Saudi Arabia and his ancestral homeland in Yemen.
The group has exploited instability in impoverished Yemen since a 2011 uprising forced president Ali Abdullah Saleh to step down.