CNN quoted a US Secret Service official as saying that multiple shots were fired on a public road outside an established security perimeter, and heard by Secret Service personnel posted at the residence.
The incident occurred at about 2025 EDT (0125 GMT).
Searches were due to be conducted outside the home and nearby residences in New Castle County to see if any buildings were hit by bullets, CNN said.
The vice president's residence is several hundred yards from the main road from where the shots were fired. The Secret Service said that local police arrested an individual in a vehicle that attempted to pass an officer who was securing the outer perimeter of the area.
The individual is not currently tied to the incident, CNN said, but a Secret Service official told the television network the individual would be questioned about the incident.
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