"There were no injuries to any Secret Service or White House personnel and the cause and manner of the crash remain under investigation," the statement said.
Secret Service spokesman Anthony Guglielmi later said in a tweet that a "preliminary investigation reveals the driver may have intentionally struck the security barriers at Lafayette Square", adding that charges would be filed over the incident.
A local CBS affiliate, WUSA9, reported that what appeared to be a Nazi flag had been found during a search of the U-Haul, though no other information on the flag was provided.
The crash took place just before 10 pm (0200 GMT) on the northern edge of the square, a few hundred yards from the White House in an area home to several upmarket hotels.
A local Fox affiliate reported that some hotel guests said they had been told to evacuate after the crash.
A journalist with the station posted video from the scene showing a robot searching the cargo area of the truck.