There was no word on a motive, but police say the inside of the SUV and the driver were deliberately doused with gasoline.
Investigators say the vehicle crashed into the building at Connecticut and L streets, N.W., around 7:45 p.m. Friday. Officials said the building located less than a mile from the White House and in the city's business district, has a mix of offices, retail shops and restaurants. One floor above, a restaurant was crowded with Friday evening diners.
The FBI's Joint Terrorism Task Force has been called in to help with the investigation.
The driver was taken to a hospital with minor injuries.
The Associated Press contributed to this report.