Dr Margaret Connolly, the sister of President Catherine Connolly, is among at least six Irish citizens aboard an aid flotilla that have been detained by Israel, organisers say.
They said the interception happened around 70 nautical miles off Cyprus.
The Global Sumud Flotilla said it has lost contact with the intercepted boats.
The flotilla has posted videos from Dr Connolly and five others, which appear to have been recorded in advance of their detention.
In her video, Dr Connolly said: "If you are watching this video, it means I have been kidnapped from my boat in the flotilla by the Israeli occupying forces, and I'm now being held illegally in an Israeli prison.
"I am so proud to be taking part in this flotilla -it is the largest to date."
Israel's foreign ministry earlier said on X that it will not allow any breach of its naval blockade on Gaza.
As Israeli military vessels intercepted the flotilla fleet, the Global Sumud Flotilla demanded safe passage for its "legal, non-violent humanitarian mission".
It called on international governments to stop what it called illegal acts of piracy on the part of Israel.
Karen Moynihan, head of the Irish delegation for the Global Sumud Flotilla, who is not on board, said 15 Irish citizens are sailing in the flotilla.
Watch: Moment Israeli forces boarded one of aid flotilla vessels
The flotilla organisers could not confirm how many, if any, of the Irish sailors have had their ships intercepted.
Ms Moynihan has called on the Irish Government to condemn the interception and demand safe passage for the people who are legally entitled to sail in those waters.
The flotilla organisers also posted a video showing boats approaching their flotilla.
One video featured Irish citizen Mikey Cullen.
Ships from the Global Sumud Flotilla had set sail for a third time on Thursday from southern Turkey, after earlier attempts to deliver aid to Gaza were intercepted by Israel in international waters.
In its statement, Israel also called on "all participants in this provocation to change course and turn back immediately".
The previous flotilla departed from Spain on 12 April.
But Israeli forces intercepted vessels in that group, taking more than 100 pro-Palestinian activists to Crete and detaining two others in Israel.
Additional reporting Reuters
