There is no indication the incident specifically targeted the music superstars, police say.
Officers told Page Six the driver appeared to be "confused" and made no threats or references to the couple before he was taken into custody.
Beyonce, 44, and Jay-Z, 56, own the seven-bedroom waterfront property in East Hampton in New York state, which they bought in 2017.
According to Page Six, Detective Sergeant Jennifer Dunn said about the 63-year-old house crash suspect: "He has no criminal history and he seemed confused at the scene and after the arrest.
"He did not make any threats or mention names of the residents.
"It could just be chance he picked that house if he was having a medical issue."
According to a police report obtained by the publication, the man from the Bronx in New York City was allegedly "driving at a high rate of speed up the driveway" before failing "to stop at the closed mechanical driveway gates", causing what officers described as "significant damage".
Police said the driver was arrested before being taken to hospital complaining of pain.
Authorities impounded the vehicle involved and completed criminal trespass and criminal mischief affidavits while the investigation continues.
Dunn also told Page Six the man had stopped at another property in the area before arriving at the estate.
She said the homeowner reported the man had asked for a woman by name before leaving when told she did not live there, adding that the resident also believed he seemed confused.
5°C