Shares of the Miami-based company were down 2.1% on Monday to $16.93.
Major cruise operators haven't been sailing in the U.S. for about six months due to the coronavirus pandemic shutdown.
Norwegian said the suspension includes its three cruise brands, Norwegian Cruise Line, Oceania Cruises and Regent Seven Seas Cruises.
"The company will continue to work in tandem with global government and public health authorities and its Healthy Sail Panel expert advisors to take all necessary measures to protect its guests, crew and the communities visited," Norwegian said in a statement.
The news follows Friday's announcement that President Donald Trump had tested positive for the coronavirus. White House officials said Trump was anxious to be released Monday after three nights at Walter Reed National Military Medical Center.
Last week, the Centers for Disease Control and Prevention extended its ban on cruise sailings in the U.S. to Oct. 31 instead of into next year.
Robert Redfield, the director of the Centers for Disease Control and Prevention, reportedly was overruled when he pushed to extend a "no-sail order" on passenger cruises until February 2021 because of the virus' severity and the vulnerability for spread on cruises.
Health officials have complained the decision was politically motivated because the cruise industry is a major economic presence in Florida, a key battleground state. The White House has denied the allegation.
The cruise ship industry, which voluntarily set the Oct. 31 suspension date, was a flash point for the coronavirus outbreak.
The CDC said there have been at least 3,689 Covid-19 or coronavirus-like illness cases on cruise ships in U.S. waters, "in addition to at least 41 reported deaths."