Fire trucks surrounded the Boeing 777, which had taken off from Beijing, after it landed early in the afternoon, spraying fire retardant foam around the aircraft.
Two of the plane's giant wheel units were ripped from the craft during the landing and could be seen on grass near the runway.
Passenger Paul Venter said the trouble started as the aircraft was about to land.
"The wheels came out and went for touchdown, and the next moment we just dropped. I couldn't tell you how far," he said.
"I didn't speak to the pilot, but I saw him, and he looked very pale," Venter said.
The plane's wheels appeared to collapse as it came down in the grass in front of the airport's southern runway, witness John Rowland told the British Broadcasting Corp.
"It crashed into the runway, debris was flying everywhere, there was an enormous bang and it skidded sideways," he said.
London Ambulance Service said eight people had been taken to a hospital with minor injuries.
The accident at one of Heathrow's two runways occurred just before a plane carrying British Prime Minister Gordon Brown and a delegation of business leaders, including Virgin Chairman Richard Branson, was about to depart for China. The prime minister's plane was about half a mile away.
More than 200 flights were canceled - nearly a fifth of the day's flights, airport operator BAA said. Planes were still able to take off and land on Heathrow's northern runway, air traffic control company Nats said. Some other flights were diverted to other airports.
The Air Accident Investigation Branch was investigating, British Airways Chief Executive Willie Walsh told reporters, adding the airline didn't want to speculate on the cause.
It was the first accident involving the Boeing 777, a mainstay of many carriers' fleets, since the plane entered service in 1995, said Boeing spokeswoman Liz Verdier in Seattle.
The Boeing 777 was relatively new at six years old, Walsh said, adding the pilot was one of BA's most experienced having worked for the company for nearly 20 years.
The plane's engines were louder than normal, said Neil Jones, a witness and licensed pilot.
"The aircraft was banking to the left and it was coming in very low over the surrounding houses," he said.
Passenger Jerome Ensinck told the BBC that he at first thought the plane had made a hard landing.
"There was no indication that we were going to have a bad landing," he said. "When we hit the ground it was extremely rough."
"Then the emergency exits were opened and we were all told we should go through as quickly as possible, and the moment I was away from the plane I started to realize that the undercarriage was away, and we had missed the runway, Ensinck said.
"Now I realize I've had a close call," he said.
Robert Cullemore of Aviation Economics, a London-based aviation consultancy, said a pilot from a competing airline told him officials believed the cause of the accident was wind shear, a sudden gust of wind.
"It can happen anytime anywhere and if it happens you just hope there is no airplane nearby," Cullemore said.
He said the pilot kept the plane in the air long enough to prevent a disastrous outcome.
"If it had landed 200 meters (656 feet) shorter than it did, it may have hit perimeter fence and obviously some other buildings and the car park, clearly we would be dealing with fatalities and obvious damage," Cullemore said.
There are a few other possibilities, said Timothy Crowch, an aviation analyst with 35 years of experience as a commercial pilot.
The landing gear punched through both wings, indicating a "massive vertical impact." That suggests a total loss of engine power may have been the cause, he said