The Global Sumud Flotilla said it was attacked during the night by "unidentified drones and communications jamming".
It said "at least 13 explosions" were heard on and around several flotilla boats, while drones or aircraft dropped "unidentified objects" on at least 10 boats.
No casualties were reported but there was damage to the vessels and "widespread obstruction in communications", it said on Wednesday.
Activists posted a brief video on the flotilla's social media account showing what appeared to be an explosion on or near one of the vessels.
Greece's coast guard did not report any distress calls.
The Israeli military did not immediately respond to questions regarding the attack.
Italy condemned the attack and activated a navy frigate to be on hand for possible rescue operations, Italian Defence Minister Guido Crosetto said.
Crosetto said the Italian Navy's frigate Fasan, which was sailing north of Crete, was "already heading towards the area for possible rescue operations".
Italy has informed Israel about the decision.
"In a democracy, demonstrations and forms of protest must also be protected when they are carried out in accordance with international law and without resorting to violence," Crosetto said.
Italy had warned Israel to respect the rights of Italian activists taking part in the flotilla.
Foreign Minister Antonio Tajani said 58 Italians were taking part in the flotilla, including some MPs.
Swedish activist Greta Thunberg, who is on board one of the flotilla boats, called the strikes a "scare tactic" and implored the flotilla's supporters to stay focused on Gaza rather than on the activists sailing in the Mediterranean Sea.
"We were aware of the risks of these kind of attacks and that's not something that's going to stop us," Thunberg said on a livestream on Wednesday morning.
Simone Zambrin, an Italian activist with the flotilla, said drones "have been flying over our heads for days now" and on Wednesday "dropped devices at our boats, damaging both the sails and the hearing of some of our crew members".
The flotilla, comprised of dozens of boats from several countries, is carrying a symbolic amount of humanitarian aid, including food and medicine, for Palestinians in Gaza.
The Israeli foreign ministry accuses organisers of being linked to Hamas, and says it has proposed that the activists unload their aid in the Israeli port of Ashkelon for it to be transported into Gaza.
"Israel will not allow vessels to enter an active combat zone and will not allow the breach of a lawful naval blockade," the ministry said on Monday.
The flotilla has reported several attacks since it set sail from Spain on September 1, including two while some of its boats were in Tunisian waters.