Fellow passengers claimed the overhead locker "burst open" as the plane was taxiing down the runway and reported hearing a "terrible sound" as the man fell to the floor after being struck. "It was a freak accident".
The man is said to be "fighting for his life" after the freak accident on a Bangkok-bound jet waiting to take off from Heathrow Airport.
The incident happened on British Airways Flight 9 from London to Bangkok.
"He was taken to a local hospital and we wish him a speedy recovery".
In a statement, the airline said: "We take the health and safety of our customers very seriously and our cabin crew receive extensive training to deal with incidents on board".
London Ambulance Service said a man was treated for a head injury and was taken to hospital as a priority patient following the incident on Monday afternoon.
Paramedics rushed to the scene to treat the seriously injured man who was taken to Hillingdon Hospital in Uxbridge.
British Airways' carry-on luggage restrictions have a maximum size of 22 in x 18 in x 10 in, and a maximum weight of 51 pounds - heavy if it's coming from above.
British Airways stipulates in its rules and regulations that passengers' hand luggage must weigh no more than 23kg and must be able to fit into the overhead lockers of the plane. While the plane was still at the gate, an overhead storage unit came open and one of the bags inside fell out onto the passenger.