"Dear customer, due to extreme demand, we are closing our website for a short time in order to increase capacity and stability," the airline said in a statement on Thursday.
Norwegian announced earlier on Thursday that it was extending its budget service to longer haul destinations.
New York City has been launched as the first destination, with flights commencing from Stockholm's Arlanda in May 2013, followed by Bangkok in June.
Tickets to JFK airport in New York could be had for a paltry 1,199 kronor, with the return journey costing 964 kronor, including taxes and fuel surcharges.
"Today's launch is a major and important milestone in Norwegian's history," the company's CEO Bjørn Kjos said in a statement on Thursday morning.
The company promises to adapt its no-frills service to offer customers "that little extra" to provide more comfort on the longer haul routes.
Norwegian's website was back up and running by 4pm on Thursday afternoon, but at first glance there appeared only a handful of the cut-price tickets still available.
The routes will be plied by Boeing 787 Dreamliner aircraft, the first of which will be delivered to the airline in April 2013.