Military jets scrambled to intercept the aircraft and fired warning flares.
Two men in the aircraft later were taken into custody at a Maryland airport where the plane landed after a military escort, said Capitol Police Chief Terence Gainer.
"This appears to be errant pilots," he said, adding that officials were concerned because the plane appeared to be "on a straight-in shot toward the centre of the Washington area".
White House spokesman Scott McClellan said the plane came within three miles of the White House. President Bush was not there at the time.
Security officials in several other government buildings, including the Treasury Department and the US Supreme Court, ordered people to safer locations.
White House evacuated
Bush was biking at Patuxent Wildlife Research Center in suburban Maryland, McClellan said.
Vice President Dick Cheney, in the White House, was moved to a secure location elsewhere, said a senior administration official.
First lady Laura Bush and former first lady Nancy Reagan, who is staying at the White House for a special event at the Reagan building, also were evacuated and taken to a secure location.
Police and Secret Service officers
were deployed after the alert
Congressional leaders were hustled from the Capitol by armed officers. The threat level at the White House was raised to red - the highest - for eight minutes.
The incident began at 15:28 GMT when Federal Aviation Administration radar picked up the aircraft, a small two-seater Cessna 150 with high wings, officials said.
The aircraft breached the security zone over Washington, law enforcement officials said, prompting alerts across the city.
September 11 attacks
Gainer said the first alert went out when the plane was 17 minutes from the city.
Two Black Hawk helicopters were dispatched at 15:55 GMT from Reagan National Airport, according to an FAA official.
The plane was also approached by two F-16 fighter aircraft, scrambled from Andrews Air Force Base.
President George Bush was not in
Washington during the alert
The military aircraft escorted the plane to the Frederick Municipal Airport in Frederick, Maryland.
The incident sparked a flurry of emergency activity throughout the capital, which was targeted on 11 September, 2001, and has been under a heightened state of alert since then.
In the 3½ years since the attack, hundreds of small planes have flown within the restricted airspace around the capital - a 25km radius around the Washington Monument.