Dublin-based club Bohemians tabled the resolution, saying Israel violated two provisions of the UEFA statutes.
The motion was carried by 74 votes to seven with two abstentions.
In a statement, the FAI said they will now "submit a formal motion to the UEFA executive committee requesting the immediate suspension of the Israel Football Association from UEFA competitions".
The two alleged breaches of UEFA statutes refer to "organisation of clubs in illegal settlements in the occupied West Bank without the consent of the Palestinian Football Association" and the "failure of the IFA (Israel Football Association) to implement and enforce an effective anti-racism policy".
Israel's national and club teams compete in UEFA's competitions, but have largely played their home matches in neutral venues since the 7 October attacks in 2023 on security grounds.
Similar calls from Turkish and Norwegian football bosses for Israel to be suspended from international competition had eased since the announcement of the Israel-Hamas peace plan for Gaza last month.
Bohemians said in a statement they were "proud" to have advanced the motion and expressed gratitude to those delegates who had voted in favour.
American Republican senator Lindsey Graham criticised the move, claiming it would be "punishing the Jewish people 80 years after the Holocaust because they choose to fight back against terrorist groups".