The Secret Service, which is in charge of the president’s security, said the vehicle followed the motorcade past a security barrier about 200 meters (650 feet) from the White House.
The driver, 55, was arrested and has been charged with unlawful entry, said Secret Service spokesman Edwin Donovan.
The vehicle “was immediately stopped by Uniformed Division officers,” and subsequently investigated, Donovan said.
The White House declined to comment but a law enforcement official told AFP on condition of anonymity that the motorcade was that of the Obama daughters, Malia and Sasha, who were reportedly on their way home from school.
Reporters working in the White House were not allowed to leave the building for an hour in the afternoon until the lockdown was lifted.