Biden and his wife were not at home at the time of shooting, which occurred at about 8:25 pm on Saturday, according to the Secret Service, Xinhua reported.
"The shots were heard by Secret Service personnel posted at the residence, and a vehicle was observed by an agent leaving the scene at a high rate of speed," Secret Service spokesperon Robert Hoback was quoted as saying.
An individual in a vehicle was arrested about half an hour later for attempting to pass a police officer who was securing the outer perimetre of the area in New Castle County, Delaware, Hoback added.
The New Castle County Police, however, said on Sunday that the man was not charged in related to the shooting.
The vice president and his wife, as well as President Barack Obama were briefed on the incident Saturday night.
Thorough searches will be conducted on the outside of Biden's residence and vicinity to see if any rounds hit any structure, as the vice president's residence is several hundred yards away from the main road from where the shots were fired, media reports said.