The closure marks a sorry end to the carrier's attempt to operate budget transatlantic flights from the capital, which it launched less than two years ago.
Passengers booked between Edinburgh and Stewart, in New York state, are being flown via other airports instead.
Norwegian was due to scrap the route on 29 March, which operated four times a week and started in June 2017.
It follows the airline's flights from Edinburgh to Providence in Rhode Island ending last October, and to Bradley in Connecticut last March.
The airline has blamed the moves on the Scottish Government's failure to halve air passenger duty, chargeable on US-bound flights, from £75 per passenger to £37.50.
However, the premature end to the Stewart service was prompted by the Civil Aviation Authority banning Boeing 737 Max flights last week following an Ethiopian Airlines crash. killing all 157 on board.
A Norwegian 737 Max based at Edinburgh remains grounded at the airport.
An airline spokesman said: "Customers have already been informed that these flights will not operate following the requirement to suspend operations of the 737 Max by the aviation authorities.
"We are rerouting affected passengers on to other Norwegian long-haul services and we apologise to customers for the inconvenience."
Norwegian is also closing its crew and aircraft base at Edinburgh Airport along with two of its five other routes from the capital, to Barcelona and Tenerife.
The reductions will halve Norwegian’s route network from Edinburgh from six to three - to Copenhagen, Oslo and Stockholm.
The Ethiopian crash, near Addis Ababa on 10 March, was the second fatal accident involving a 737 Max within five months.
A Lion Air plane crashed off the coast of Indonesia last October, in which all 189 on board killed.
Investigators suspect incorrect sensor readings feeding into a new automated flight-control system may have played a role in the Indonesian crash, and the Ethiopian plane had a similar, erratic flight path.
Boeing began working on an upgrade to software behind the flight-control system shortly after the Lion Air crash and said it was close to finishing the update.
It is also working on changes in pilot training to help crews respond to faulty sensor readings.
A spokesman for Edinburgh Airport said: “This is clearly disappointing news for the airport and passengers, but the reality is we wouldn’t be facing this issue if the Scottish Government had delivered on its manifesto pledge to cut APD.
“The failure to deliver on that promise has seen an airline withdraw several long-haul routes that were delivering connectivity to and from Scotland, contributing to tourism revenue and creating jobs.
“Yet again we urge the Scottish and UK Governments to come together and find a solution that will allow Scotland’s aviation sector to compete with other nations across the world and deliver economic growth.”