Menachem Fetter (later Elon) was born in Düsseldorf, Germany, into a religious Jewish family from Hasidic backgrounds. Elon's family fled to the Netherlands a year before Nazism's ascent in Germany. In 1935, Elon's family immigrated to Palestine. In 1938, he studied Halakha (traditional Jewish law) in the Hebron Yeshiva, and was ordained as a rabbi by chief rabbis Ben-Zion Meir Hai Uziel and Yitzhak HaLevi Herzog. He was among the founders of a yeshiva high school
Midrashiat Noam in Pardes Hanna, and served for two years as a teacher there, and became one of the founders of the religious Kibbutz Tirat Zvi in the Beit She'an Valley.
The Elon family, a member of the religious Zionist elite, is entrenched in the world of law, politics, Literature, and Halakha (Jewish religious law). In 1949, Menachem Elon married Ruth Buchsbaum, the daughter of Dr.
Mordechai Buchsbaum, an Orthodox Jewish attorney and a former deputy mayor of Jerusalem. Amongst Elon's five children are Rabbi Binyamin Elon (married to writer Emuna Elon), a former member of Knesset and cabinet minister (Minister of Tourism, 2001–2004); Rabbi Mordechai Elon, the former head of Yeshivat HaKotel;
Joseph ("Sefi") Elon, a district judge in Be'er Sheva and temporary judge of the Supreme Court of Israel (2007–2009); and Ari Elon, who is secular and a lecturer on the Bible.