The vessel is carrying Miss Thunberg and her father Svante 3,000 miles to Portugal where she will go onto attend the COP 25 climate change talks in Madrid.
Ms Thunberg rose to prominence after she started spending her Fridays outside Sweden's parliament in August 2018, holding a sign reading "school strike for climate".
As she makes her way to Madrid for the U.N conference on climate change, Thunberg used the opportunity in front of reporters and supporters to emphasize the importance of working together to tackle the climate change problem and ensure livable conditions for the future of humankind.
Having used her appearance in NY to denounce governments for failing to act with sufficient urgency on the environment, Thunberg attended weekly green protests in several USA cities before embarking on her long trip home.
"People are underestimating the force of angry kids", the 16-year-old Swedish activist told crowds in Lisbon, Portugal.
Carolina Schmidt, environment minister of Chile, which is chairing the negotiations, said she hoped Thunberg's presence would galvanise more ambitious commitments by governments at talks aimed at bolstering the 2015 Paris Agreement to avert catastrophic temperature increases.More news: Kamala Harris Dropping 2020 Presidential Campaign
More news: New Zealand draw second Test against England, win series
More news: Black Widows past comes to light in prequel: Watch new teaser trailer
One person said this to the teen: "I have never in my entire life seen or heard a young lady of your age so mature, so well-grounded, such an incredible leader ( thank dear God this whole world has you to lead us all!), your so extremely articulate, passionate for your/our imperative, urgent cause for life & saving our world & planet!"
Members of the global group Extinction Rebellion held up a banner in Russian that read: "Climate Crisis".
"But also in a sense we have gone a few more months without real action being taken and without people realising the emergency we are in".
Others dressed in red robes with their faces whitened to symbolize the human species' peril danced briefly before police moved in to end the protest.
Meanwhile, the United Nations weather agency released a new report showing that the current decade is likely to set a new 10-year temperature record, providing mounting evidence that the world is getting ever hotter.
Levels of greenhouse gases including carbon dioxide hit record levels a year ago, the World Meteorological Organisation has said. "In contrast a large area of North America has been colder than the recent average", the United Nations said.