The ship left the Cypriot port of Larnaca on Monday
Israeli forces have boarded a ship trying to carry aid and pro-Palestinian activists to the Gaza Strip in defiance of Israel's blockade of the territory.
The 20 passengers include former US congresswoman Cynthia McKinney and Nobel Prize winner Mairead Maguire.
The activists also include some Britons, campaigners said.
Ms McKinney described it as "an outrageous violation of international law", as the boat was on a humanitarian mission and was not in Israeli waters.
The Israeli military said the boat was trying to enter Gaza illegally.
The US-based Free Gaza Movement has breached the blockade five times since August 2008.
Two other attempts by the activist group were stopped by Israeli warships during Israel's three-week military offensive in Gaza in December and January.
Israel keeps a tight hold on Gaza, which is ruled by the militant Palestinian group Hamas.
The Israeli military said the passengers and crew of the Greek-registered ship Arion would be handed over to immigration authorities in Ashdod, and its humanitarian aid cargo would be taken to Gaza by road after a security check.
"An Israeli navy force intercepted, boarded and took control of the cargo boat Arion... as it was illegally attempting to enter the Gaza Strip," a military spokesman said.
The British Foreign Office said on Tuesday it was aware of the situation and was trying to clarify the facts.
"We would be concerned if the stories of the Israeli Navy boarding the boat in international waters were true," a spokesman said.
"We have made it clear to Israel that we are very concerned for the safety of British nationals."
The mission is the latest by the Free Gaza Movement, which has renamed the ferry Spirit of Humanity.
"This is an outrageous violation of international law against us. Our boat was not in Israeli waters, and we were on a human rights mission to the Gaza Strip," said Ms McKinney in a statement.
"President [Barack] Obama just told Israel to let in humanitarian and reconstruction supplies, and that's exactly what we tried to do. We're asking the international community to demand our release so we can resume our journey."
On Monday, a report by the International Committee of the Red Cross described the 1.5 million Palestinians living in Gaza as people "trapped in despair", unable to rebuild their lives after Israel's offensive.
Donors have pledged $4.5 billion for reconstruction and rehabilitation in Gaza following the 22-day offensive.
According to the United Nations, the military campaign left more than 50,000 homes, 800 industrial properties and 200 schools damaged or destroyed, as well as 39 mosques and two churches.