• Norwegian Cruise Line filed a lawsuit, hoping to put an end to the state's law preventing businesses from requiring customers to show proof of Covid-19 vaccination.
• Without a lifting of the ban, the company says it could be forced to cancel cruises.
• Norwegian's first sailing from Florida is set for Aug. 15.

Norwegian Cruise Line filed a lawsuit against Florida's surgeon general, hoping to put an end to the state's law preventing businesses from requiring customers to show proof of Covid-19 vaccination.

Norwegian asked the U.S. District Court for the Southern District of Florida to throw out the state's ban and grant the company a preliminary injunction that would allow it to resume sailing with the health and safety protocols it developed in order to comply with guidance from the Centers for Disease Control and Prevention.

In the court filing, Norwegian said the state's ban hurts its ability to prevent the spread of the virus onboard its ship. As a result, it could be forced to cancel upcoming cruises, which would result in a "devastating, unrecoverable loss."

The company said it would like to require passengers to show proof of vaccination, but that would violate Florida's law and open the company up to prosecution and fines of up to $5,000 per passenger, which it cannot afford.

"We believe Florida's prohibition is on the wrong side of federal law, public health, science and is not in the best interest of the welfare of our guests, crew, and the communities we visit, therefore, we have reluctantly turned to the courts for relief," the company said in a statement to CNBC. "Our policy of 100% vaccination of guests and crew is consistent and in place without issue in every port we sail from around the world except for Florida."

In the court filing, Norwegian claimed the law violates the First Amendment by blocking communications between a business and its customers; illegally disrupts the proper flow of interstate and international commerce without substantial state interest; and violates the Fourteenth Amendment by preventing a company from protecting the health and safety of its employees and customers against the pandemic.

The cruise industry is among one of the last sectors to return to pre-pandemic operations. At the beginning of the health crisis, there were several high profile outbreaks on ships, and public health agencies are trying to prevent a repeat of this scenario. The CDC recently allowed the cruise line to begin sailing again with strict health protocols.

Royal Caribbean Cruises and Carnival Cruises have resumed sailings out of Florida. For those trips, the two cruise lines require unvaccinated passengers to follow safety protocols and purchase travel insurance that covers Covid-19 related costs.

Shares of Norwegian closed Tuesday down 4.4% at $26.09. The stock has fallen nearly 2.6% year-to-date.

Norwegian's first sailing from a U.S. port is scheduled for Aug. 7 and its first sailing from Florida is set for Aug. 15.

"Demand for [Norwegian] cruises has been returning in recent months, but [the company] still faces challenges in maintaining confidence in safety among its customers, especially because those customers tend to be older in age," Norwegian told the court.