Shocked passengers reported the plane being pushed back from the gate today when it hit the perimeter fence.
Ground crews were manoeuvring the large aircraft around the Sussex airport when they pushed it too far back.
The Boeing 787 plane sustained damage on its tail cone, with a picture showing the metal part being badly dented.
Passengers had to disembark the jet, which was due to fly from Gatwick to New York, due to the damage and were due to be put on a replacement aircraft.
One passenger wrote on Twitter: “Tug pushes Norwegian 787 Dreamliner back to far that it hits part of Gatwick Airport perimeter fence.
“Fire crews on precautionary standby.”
A spokesman for Norwegian Air confirmed: “We can confirm that one of our aircraft sustained some damage upon pushback on today’s flight DI7017 from London Gatwick to New York JFK.
“All passengers disembarked the aircraft as normal and are currently being assisted by our ground staff in the terminal.
“The safety and wellbeing of our customers is our top priority and we are currently making arrangements to put passengers on a replacement aircraft that will depart this afternoon.
“We would like to apologise to our customers for the inconvenience.”
The drama comes after British Airways passengers faced flight chaos last week when an IT problem delayed 300 flights and 15,000 holidaymakers.