The boat, named Irene, left the port of Famagusta in the Turkish-held north of the divided eastern Mediterranean island carrying eight activists, including three crew, and two journalists.
Holocaust survivor Reuven Moshkovitz, 82, said she felt duty-bound to attempt the voyage, which is expected to take around 36 hours.
"It is a holy duty for a survivor like me to protect against the persecuting and closing and oppressing of so many people, including 800,000 children in Gaza," she said.
Israeli defense minister Ehud Barak previously warned that Israel would intercept any ship nearing Gaza, which is run by the Islamist movement Hamas.