Tunisia's former president Moncef Marzouki is among the campaigners.
The activists said they wanted to draw attention to the blockade, which Israel says is a necessary security measure.
Israel says it acted in international waters to prevent the "intended breach of the maritime blockade" imposed since 2009 against the Hamas-run territory.
There was no violence as the navy searched the boat, Israel says.
The activists said the vessel was carrying humanitarian aid, including medicine and solar panels.
The boat intercepted on Monday is believed to be Marianne - the lead vessel of a four-strong flotilla.
"In accordance with international law, the Israeli Navy advised the vessel several times to change course," the military said in a statement, the AFP news agency reports.
"Following their refusal the Navy visited and searched the vessel in international waters in order to prevent their intended breach of the maritime blockade of the Gaza Strip."
The vessel is currently being escorted to the port of Ashdod.
The flotilla is the latest in a number of protest voyages against Israel's maritime blockade.
In 2010, nine Turkish activists were killed aboard another vessel amid clashes as Israeli commandos boarded the boat.
Ten Israeli soldiers were injured in the incident on the Turkish-owned ship Mavi Marmara as it attempted to breach the blockade.
It caused a deep rift between Israel and Turkey, who were former allies.

Lagavulin is launching a single cask edition of 522 bottles of its single malt to raise funds for local projects.
Sales of the £1,494 bottles are set to see £310,000 donated to Islay Heritage to help build a story of the island's past based on its archaeological sites.
The Finlaggan Trust, which maintains the historical home of the Lord of the Isles, should also receive £60,000.
The Lagavulin 200 Legacy is set to make further contributions to the local swimming pool, cyber cafe and arts and festival organisations, as well as a new partnership with the RSPB to restore and conserve peatlands on the island.
Nick Morgan, of Lagavulin's owners Diageo, said: "We have had a fantastic year celebrating the 200th anniversary of Lagavulin, both on Islay and with the hundreds of thousands of people around the world who adore the whisky.
"Islay and its remarkable local community are at the heart of Lagavulin.
"That's why we were determined there should be a legacy from the anniversary which would directly benefit the island and its people.
"We believe that our contribution to Islay Heritage is not only of great significance to the island itself but is an important contribution to conserving and promoting the history and heritage of Scotland."
Bottles of the Lagavulin 1991 Single Malt Scotch Whisky cask can only be purchased through an online ballot on The Whisky Exchange.
The first bottle will be auctioned separately to raise more charitable funds, and one bottle will be donated to the Diageo Archive and the Whisky Exchange.
Steven Mithen, trustee of Islay Heritage and professor of archaeology, said: "Islay Heritage is hugely grateful to the Lagavulin 200 Legacy for the support it is providing to further our knowledge about the archaeological sites and monuments on Islay.
"This investment in our heritage will greatly benefit both the local community and visitors to the island.
"While some of Islay's sites and monuments are very well known and accessible, others are virtually unknown, difficult to find and rarely visited.
"There are no doubt many more waiting to be discovered which will help tell us more about not only Islay's story but that of Scotland, Europe and the path of human culture as a whole.
"We are delighted that Lagavulin shares our vision to reveal Islay's past so that it can be explored and enjoyed by everyone."
The Israeli Navy has intercepted a Gaza-bound vessel sailed by pro-Palestinian activists and diverted it to an Israeli port, the military says.
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A whisky distillery plans to invest £580,000 in community projects to mark its 200 years on the island of Islay.