The Israeli government denied any threats were made, or that any shots were fired, but said they warned the boat not to cross into Gazan waters.
The boat had set off from Cyprus on Monday, carrying humanitarian supplies for Gaza, which remains under an Israeli blockade.
Humanitarian crisis
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.
"We need to up the ante and to mount more actions and convoys of this nature," she said.