Karin Pally, spokeswoman for the group, told the AFP news agency: "The boat is coming back to Larnaca for repair after mechanical trouble during the journey."
The generator failed three hours into the 24-hour trip, forcing the boat to head back to port to the Gaza Strip.
The boat has 34 passengers on board, including six doctors and parliamentarians from Greece, Belgium and Spain. They were taking dried food, flour, baby formula, nappies and urgently needed medical supplies.
Aid mission 'risky'
"A marine engineer is waiting at the port to see what needs to be done," Pally said.
Vangelis Pissias, an organiser, told the passengers to reassemble early on
Tuesday for another try if repairs are completed.
Israel's transport ministry issued a statement calling the attempt to reach Gaza "provocative and risky".
This is the second sailing since Israel began its assault on Gaza on December 27.
The journey was a renewed attempt to break Israel's blockade of the Gaza Strip and comes after another vessel, Dignity, was damaged by Israeli naval vessels.
Joan Josep Nuet, a Spanish member of parliament, said: "We have to try to break the siege of Gaza and, at the same time, condemn what's going on."
Humanitarian crisis
In December, the group's mission failed after its boat was damaged when it collided with an Israeli naval ship.
Free Gaza organisers accused the Israelis of ramming the boat, but Israeli officials said the collision occurred when the protesters' boat attempted to outmanoeuvre the Israeli vessel.
Earlier missions had successfully reached Gaza and, on each occasion, the Israeli authorities had been notified of the boat's movements.
Israel imposed a blockade on Gaza in June 2007 as a means of isolating Hamas after it won Palestinian parliamentary elections.
Since then, there have been severe shortages of basic foodstuffs, fuel and medicines causing malnutrition among children and prompting aid groups to warn of a humanitarian crisis among the population of 1.5 million.
The closure of Gaza's crossings by the Israeli and Egyptian authorities has also meant that very few Gazans have been able to leave.