The airline said the routes are no longer commercially viable.
Boeing plans to hand over the revision of the software that controls the MCAS system by September so that authorities can review it by the end of the year.
In a statement, Cork airport said they were disappointed with the news following much-publicised aircraft issues arising from the grounding of the Boeing Max aircraft.
Before the airline started its Hamilton service, Anders Lindstrom, director of communications for Norwegian's North America branch, told CBC that the flights would encourage Canadians to fly out of Canada instead of crossing the border to USA airports.
"We take a strict approach to route management and constantly evaluate route performance to ensure we meet customer demand".
Norwegian Air has announced that it will abandon its transatlantic routes between Ireland and the United States from 15 September.
CNBC reported this week in "Airlines hurt by the 737 Max grounding are scrambling to find replacement jets", "With more than 500 Boeing 737 Max planes parked all around the world, there remains a shortage of commercial jets".
"We've been informed by Norwegian that they're ceasing operations at Green", said T.G. Green spokesperson Bill Fischer on Tuesday, of the airline that bills itself as "Europe's Best Low-Cost Airline".
Norwegian Air is engaging with its 48 pilots and 86 cabin crew at its Dublin base, including their respective unions, to ensure that redundancies remain a last resort.
Customers will also be offered a full refund if they no longer wish to travel.
The carrier will continue to offer scheduled services from Dublin to Oslo, Stockholm and Copenhagen as normal.
"Our 80 Dublin-based administrative staff at Norwegian Air International and Norwegian Group's asset company, Arctic Aviation Assets, will not be affected by the route closures".
Nonstop services to Cork and Shannon ended in March with the grounding of the 737 Max aircraft and passengers were rerouted to Dublin flights out of Stewart Airport in NY and Providence.