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.
The Israeli Navy has intercepted a Gaza-bound vessel sailed by pro-Palestinian activists and diverted it to an Israeli port, the military says.