No survivors were found at the crash site, Virginia state police said.
The jet fighters created a sonic boom over the US capital as they pursued the errant Cessna Citation, officials said, causing consternation among people in the Washington area.
Four people were onboard the Cessna, a source familiar with the matter said. A Cessna Citation can carry seven to 12 passengers.
After several hours first responders reached the crash site but found no one alive, the Virginia State Police said in a statement.
The Cessna was registered to Encore Motors of Melbourne, Florida, according to the flight-tracking website Flight Aware.
Encore owner John Rumpel told the Washington Post his daughter, a grandchild and her nanny were on board.
"We know nothing about the crash," the Post quoted Rumpel as saying. "We are talking to the FAA (Federal Aviation Administration) now."
The US military attempted to contact the pilot, who was unresponsive, until the Cessna crashed near the George Washington National Forest in Virginia, North American Aerospace Defense Command (NORAD) said in a statement.
The Cessna appeared to be flying on autopilot, another source familiar the matter said.
"The NORAD aircraft were authorised to travel at supersonic speeds and a sonic boom may have been heard by residents of the region," the statement said, adding that NORAD aircraft also used flares in an attempt to the pilot's attention.
A US official said the fighters did not cause the crash.
The Cessna took off from Elizabethton Municipal Airport in Elizabethton, Tennessee, and was bound for Long Island MacArthur Airport in New York, about 80km east of Manhattan, the FAA said in a statement, adding that it and the National Transportation Safety Board would investigate.
According to Flight Aware, the plane appeared to reach the New York area, then made nearly a 180-degree turn.
Incidents involving unresponsive pilots are not unprecedented. Golfer Payne Stewart died in 1999 along with four others after the aircraft he was in flew thousands of kilometres with the pilot and passengers unresponsive. The plane eventually crashed in South Dakota with no survivors.
In the case of Stewart's flight, the plane lost cabin pressure, causing the occupants to lose consciousness because of oxygen deprivation.
Similarly, a small US private plane with an unresponsive pilot crashed off the east coast of Jamaica in 2014 after veering far off course and triggering a US security alert including a fighter jet escort.
On Sunday, the sonic boom rattled many people in the Washington area who took to Twitter to report hearing a loud noise that shook the ground and walls. Several residents said they heard the noise as far away as northern Virginia and Maryland.
