A military statement confirmed IDF navy soldiers boarded the Al Karama in an effort to stop it from breaking the maritime security blockade on the Gaza Strip.
It said the move had come "after all diplomatic channels had been exhausted and continuous calls to the vessel had been ignored."
The yacht was heading for Gaza despite Israeli warnings that it would intercept the ship. It was the only boat remaining from a 10-vessel flotilla that had been due to sail for Gaza at the end of June.
According to the organisers the move to board the boat came some four hours after navy boats had surrounded the French-flagged yacht in international waters, 40 nautical miles off the Gaza shoreline.
They have urged the French government "to take its responsibilities and to protect the passengers, and to call on Israel not resort to violence."
In Gaza, Hamas spokesman Taher al-Nunu angrily denounced Israel's "Zionist piracy" and blamed the United Nations for not punishing Israel over its raid on a six-vessel flotilla that set sail in May 2010, led by the Mavi Marmara.
The raid left nine Turkish activists dead and prompted international criticism of Israel and a breakdown in ties with Ankara.
Israel insists its blockade is both legal and necessary to prevent Hamas from obtaining funds and weapons in order to attack the Jewish state.