Zaandam and another ship from Holland America, Rotterdam, cross the channel "under extraordinary conditions and for humanitarian reasons", a statement from the Panama Canal said Sunday.
Passengers who did not experience symptoms were transferred from Zaandam to Rotterdam on Saturday, Holland America said in a statement.
The ship could arrive in Florida on Wednesday
Holland America previously announced its intention to travel to Fort Lauderdale, but Port Everglades officials said on Sunday that passengers were not cleared to leave at that port.
It will take about three days for ships to reach South Florida as they begin to cross the channel, the Port Everglades statement said.
Holland America must submit a pre-arrival plan that addresses a long list of Unified Command requirements for entry into Port Everglades before being allowed to port, according to the statement.
The ship left Buenos Aires on March 7 and no one has been off the ship since March 14 in Punta Arenas, Chile.
Zaandam had booked transit through the channel for April 1, 2020 since April 2018, according to the channel statement.
Passengers and crews with flu-like illness
A total of 189 people – 73 guests and 116 crew members – on board Zaandam are suffering from flu-like symptoms as of late Sunday night, according to a statement from Holland America.
Some on board the ship say the situation is serious and passengers have been confined to their state room for several weeks.
The parents of Maximilian Jo, Jae, 76, and Julitta, 75, are both on board Zaandam.
Jo told CNN in an email Sunday that his father suffered from fever for hours before he was brought to Tylenol by the crew. He has communicated with his parents via email, he said.
The couple, from Long Island, New York, departed the ship March 7 days before the cruise line announced they would halt the global operation, Jo said.
They had considered not going on a cruise, but when they reached Holland America, they were told that no refund for the scheduled trip would be provided, according to Jo.
Another passenger on the ship, Clifford Kolber, told CNN Friday that he and his wife have been isolated on Zaandam since last Sunday. Both have existing relationships.
He hopes they will be able to add to the quay before they get worse.
"We just want the ports in the country to help us because we don't want more people to die," Kolber said.
CNN's Sara Weisfeldt, Stephanie Gallman, Rosa Flores and Melissa Alonso contributed to this report.