The suit, a copy of which was obtained by technology blog TechCrunch, was filed in DC Superior Court by Larry Klayman, who describes himself in the complaint as "an American citizen of Jewish origin" who is "active in matters concerning the security of Israel and all people".
Klayman also identifies himself as the founder of Freedom Watch, whose website describes it as a political advocacy group dedicated to protecting privacy, free speech and other rights and "our national sovereignty against the incompetent, terrorist state-controlled United Nations".
Facebook dismissed the case as "without merit" and said it would fight.
"While we haven't been served with a complaint, we believe the case is without merit and we will fight it vigorously," a Facebook spokesman said.
Facebook shut down the page on Tuesday, several days after Israeli Public Diplomacy Minister Yuli Edelstein sent a letter to Zuckerberg urging him to remove it.
Facebook said the page was initially tolerated because it "began as a call for peaceful protest" but direct calls for violence began appearing and the page was removed for violating Facebook's policies.
Sign up for CIO Asia eNewsletters.