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The jet was carrying 148 people, including crew, on a flight from Delhi to Bangalore, The Times of India newspaper reported.
The pilots did not realize the eight-by-four-foot panel was missing until after the flight landed, the newspaper said, adding that India's aviation authorities are investigating.
Boeing said the missing panel fell from the underside of the plane on the right side. A photo on The Times of India website showed a large opening with components and aircraft structure visible inside.
"It was the mid-underwing-to-body fairing located on the belly of the airplane on the right side," Boeing spokesman Doug Alder said. The part "provides a more aerodynamic surface in flight."