Thousands were expected to gather on the grounds for the July 4 fireworks.
The park police said Jack Joseph Dessin, 38, of New Jersey, was arrested on charges of assault with a dangerous weapon (automobile) and destruction of government property.
Photos were posted on Twitter on Saturday night of a vehicle that came to rest near a low retaining wall around the monument. Two or more signs appeared to be fastened to the vehicle. It was not clear what they said.