The shots were fired on a public road several hundred yards from the house, outside a security perimeter, at about 8:25 p.m. EST. Secret Service personnel at the residence heard the reports and saw the vehicle speeding away.
Biden, 72, who served as a U.S. senator from Delaware for more than three decades, has residences in New Castle County and in Washington, D.C.
He and his wife, Jill, were in Delaware when the shooting occurred but were out for the evening, the Secret Service said.
Authorities said they would search the area to determine whether the Biden home or other nearby residences were hit by bullets.
About half an hour after the shooting, local police arrested an individual in a vehicle that attempted to pass an officer who was securing the area. The individual is not currently tied to the incident but the Secret Service said the person would be questioned about the shooting.
The incident occurred as the Secret Service tries to recover from a series of security lapses. In September, a knife-carrying man jumped the White House fence and ran into the president’s official residence.
Last week, the agency charged with protecting the president and vice president announced that it would remove four senior officials from their jobs and retire a fifth, as part of a shake-up intended to address the problem.