A crowd of well-wishers saw off the sailing vessel Estelle as it left the Italian port as part of the "Freedom Flotilla" movement.
"We think it will take around two weeks to get to Gaza, but it will obviously also depend on the weather conditions," spokeswoman Ann Ighe told the AFP news agency.
The Estelle, whose voyage was organized by an international pro-Palestinian coalition, is carrying humanitarian goods to the Gaza Strip.
The 17 activists from around the world on board include passengers and crew from Sweden, Norway, Canada, the United States and Israel.
Israel says the blockade against Gaza is necessary to prevent weapons from entering the coastal territory, which is run by the Islamist movement Hamas.
The Free Gaza movement landed in hot water last month after its founder, Greta Berlin, tweeted that "Zionists operated the concentration camps and helped murder millions of innocent Jews."
The tweet linked to a video of Eustace Mullins, a conspiracy theorist, claiming that the word “Nazi” combines the words “National Socialist” and “Zionist.”
The organization Ship to Gaza Sweden quickly issued a statement:
"This movie link and its content have since been connected to Ship to Gaza Sweden and this year's Freedom Flotilla mission. Let's make it clear that our action is not anti-Semitic, and furthermore is not organised in co-operation with the Free Gaza Movement," the organization said.
The first Freedom Flotilla in May 2010 ended in tragedy when nine Turkish nationals were killed after Israeli commandos boarded the Turkish-flagged Mavi Marmara, the lead ship, as it tried to break through the blockade.
"When people think of flotillas, they think of the Mavi Marmara. But the Estelle is very different, she was chosen to change the perception of the campaign, to show that it's a non-violent campaign," spokeswoman Ighe said.
At just 53 metres (173 feet) long, the Estelle is much smaller than the Marmara ferry, and has sails as well as an engine.
"It is a vessel that has travelled for Greenpeace protests and on fair-trade missions. The Estelle is a peaceful ship," Ighe said.
Naples mayor Luigi de Magistris said Friday on visiting the Estelle:
"This is not an initiative in favour of Hamas but in favour of Palestine, of the Palestinians who live in Gaza, and in favour of two states living as neighbours in peace and security."
The Estelle set off originally from Stockholm and arrived in the Gulf of Naples on Thursday after a tour of Europe, including Finland, France and Spain. The crew will now attempt to reach and enter Gaza.