Another activist, Kim Ah-hyun, is reportedly travelling on a nearby vessel that the group warned could also be seized by Israel.
She was detained by Israeli forces during an earlier attempt to enter Gaza in October and was later released.
Organisers said there were 426 people taking part in the mission, among them 96 Turkish activists and participants from 39 other countries including Germany, the US, Argentina, Australia, Bahrain, Brazil, Algeria, Indonesia, Morocco, France, South Africa, the UK, Ireland, Spain, Italy, Canada, Egypt, Pakistan, Tunisia, Oman and New Zealand.
Israeli forces also attacked the Global Sumud aid flotilla off the coast of the Greek island of Crete overnight between April 29 and April 30.
