Members of the US-based Free Gaza Movement, who were on board the boat, said on Tuesday the Israeli navy threatened to open fire unless they turned the boat around.
The boat had set off from Cyprus on Monday, carrying humanitarian supplies for Gaza, which remains under an Israeli blockade.
Speaking to Al Jazeera, Caoimhe Butterly, a spokesperson for the Free Gaza movement, said: "This is the third humanitarian relief boat and solidarity mission that has been aggressively stopped by the Israeli army.
"The humanitarian situation is at crisis point. There has been a systematic and deliberate destruction of the humanitarian infrastructure of Gaza.
"We were taking medical supplies and medical equipment and limited amounts of building material ... although $4 bn has been pledged to the Gaza Strip for reconstruction ... no cement or building supplies are allowed in as a result of the siege.