It said the man approached the White House's fence on Pennsylvania Avenue just before noon local time (17:00GMT) before taking out a handgun and firing several shots.
No one else was injured, according to police.
President Donald Trump is not at the White House, but at his Mar-a-Lago estate in Florida.
The man was in a large crowd when he fired the gun, the Washington Post reports, citing witnesses.
A video posted to Twitter shows many people running away from the scene.
The man's name has not been released.
Washington DC police earlier said on Twitter that their "natural death squad" was on the scene.
Geoff Bennett, White House correspondent for NBC News, said that journalists were "sheltering" in the press briefing room.
Mr Trump is with First Lady Melania Trump in Florida. They are scheduled to return for a dinner in Washington on Saturday evening.
There have been a number of security incidents at the White House in recent years.
Most recently, on 23 February, a car drove into a security barrier outside the building. A 35-year-old woman was detained.
In March last year a man armed with pepper spray spent more than 16 minutes inside the grounds after jumping the fence.