Inside the embassy, employees heard this message over the loudspeaker: "An explosion caused by a rocket has occurred on compound."
About an hour later the all-clear was given, with no injuries reported.
There was no immediate comment from Afghan officials or those with the Nato mission, which is also nearby.
Two Taliban car bombs shook Kabul last week, killing several civilians and two members of the Nato mission.
The 9/11 anniversary is a sensitive day in Afghanistan’s capital and one on which attacks have occurred.
A US-led invasion of Afghanistan shortly after the 2001 attack toppled the Taliban, who had harboured Osama bin Laden, the al Qaida leader and attacks mastermind.
In the nearly 18 years of fighting since then, the number of US troops in Afghanistan soared to 100,000 and dropped dramatically after bin Laden was killed in neighbouring Pakistan in 2011.
Now about 14,000 US troops remain and Mr Trump has called it "ridiculous" that they are still in Afghanistan after so long and so many billions of dollars spent.
It is not clear whether the US-Taliban talks will resume.