The unidentified person fired multiple rounds from what some reports said was a high-powered assault rifle.
“This morning at approximately 2:15 am, US Secret Service officers responded to the Embassy of Cuba following reports of shots fired,” the Secret Service said in a statement.
“One individual was arrested for being in possession of an unregistered firearm as well as unregistered ammunition, assault with the intent to kill, and possession of a high capacity feed device.
“No injuries were reported at the scene.”
Washington’s police department confirmed the incident but said an investigation was in the hands of the Secret Service, which often handles investigations involving foreign diplomats.
Local media said the person arrested was a man who fired about 300 rounds from an assault rifle-type weapon.
The embassy, located on 16th Street at the edge of the Adams Morgan neighbourhood, a normally bustling area full of bars and restaurants but which has been stilled by the coronavirus shutdown.
The administration of President Donald Trump has chilled relations with Havana, reversing course after an opening initiated by his predecessor Barack Obama.
In October 2017, it expelled 15 Cuban diplomats after a rash of incidents in which US embassy staff in Cuba reported as yet unexplained head pains, dizziness and hearing loss.