A federal judge has for now sided with Norwegian Cruise Line Holdings Ltd. in its bid to invalidate Florida’s rule that bars businesses from requiring proof of Covid-19 vaccination from their customers.

U.S. District Judge Kathleen Williams in Miami on Sunday granted the cruise operator’s request for a preliminary injunction that prevents the enforcement of the Florida ban on its vessels departing from the state. The company in July sued Florida’s surgeon general, Scott Rivkees, in the U.S. District Court for the Southern District of Florida.

“While litigation is a strategic tool of last resort, our company has fought to do what we believe is right and in the best interest of the welfare of our guests, crew and communities we visit,” said Daniel Farkas, Norwegian’s general counsel.

Florida plans to appeal the judge’s decision, a spokeswoman for the state governor’s office said Monday.

“A prohibition on vaccine passports does not even implicate, let alone violate, anyone’s speech rights, and it furthers the substantial, local interest of preventing discrimination among customers based on private health information,” the spokeswoman said.

The Florida Department of Health doesn’t comment on pending litigation, a spokeswoman said.

The decision comes as Norwegian is set to offer cruises from Florida to the Caribbean starting Aug. 15. Florida is a cruise hub that in 2019 accounted for about 60% of cruise embarkations in the U.S., according to the industry group Cruise Lines International Association.

The cruise industry is treading delicately as it begins sailing again in the U.S. WSJ’s Dave Sebastian explains the complicated maneuvers the industry faces as it works to return to pre-pandemic levels. Photo: Apu Gomes/AFP/Getty Images The Wall Street Journal Interactive Edition

The company is sticking with its policy to require full vaccinations for all crew and passengers, including children, for initial sailings through Oct. 31 after more than a yearlong hiatus and billions of dollars in losses. On Saturday, Norwegian resumed its U.S. cruise from Seattle to Alaska.

Norwegian, in its lawsuit, argued that restricting the flow of information—in this case, requiring vaccine documentation—affects freedom of speech protected by the First Amendment. It also said Florida’s ban disrupts the flow of interstate and international commerce, in violation of a part in the U.S. Constitution that gives Congress the sole authority to regulate interstate commerce.

Judge Williams said in her order that Norwegian is likely to succeed on the merits in showing that the ban puts burdens on interstate commerce, as many of the ports it plans to sail to have vaccination requirements. She also said the company is likely to prevail on its First Amendment claim.

Norwegian “has demonstrated that public health will be jeopardized if it is required to suspend its vaccination requirement,” Judge Williams said. She said Dr. Rivkees didn’t provide evidence showing that the ban is effective in protecting the medical privacy of Florida residents or preventing discrimination against unvaccinated people.

Florida’s ban, made into law in May, is in place as cruise operators have been working to satisfy guidelines set by the Centers for Disease Control and Prevention. Committing to a 95% vaccination rate for crew and passengers is one way for cruise operators to get the green light from the agency, the CDC said.

The Florida attorney general has asked the Supreme Court for an emergency order blocking the CDC’s Covid-19 guidelines for cruise ships, arguing that the damage to the tourism industry outweighs their public-health benefits. The state sued in April to invalidate the guidelines, arguing they exceeded the CDC’s legal authority and were too burdensome for the cruise industry.

The spread of the Delta variant and surge in Covid-19 cases have led to disruptions in travel and leisure. The global cruise industry, derailed last year by Covid outbreaks on ships in the early stages of the pandemic, resumed sailings internationally last summer. Several cases of Covid-19 have been reported on U.S. voyages this summer, even on ships where most passengers were fully vaccinated.

In its complaint, Norwegian said the potential spread of the Delta variant is another driver of its decision to require full Covid-19 vaccinations.

Norwegian saw a slight decrease in net new booking activity in July, Chief Executive Frank Del Rio said on a conference call Friday. The cruise operator views the variant as a temporary phenomenon that isn’t likely to have lasting effects, he said.

Write to Dave Sebastian at dave.sebastian@wsj.com