Litzman was born in 1948 to Polish survivors of the Holocaust, in a displaced persons camp in Germany. When he was two years old, the family immigrated to the East New York section of Brooklyn, & then to the Borough Park section of Brooklyn, where he grew up. In 1966, at age 17, he immigrated to Israel and continued his Torah studies. His first job was as principal of the Hasidic Beis Yaakov girls' school in Jerusalem. Litzman has five children and lives in Jerusalem.
He later became active in politics under the guidance of the then Gerrer Rebbe, Rabbi Simcha Binem Alter. Over time he became known as the rebbe's right-hand man, a role he continues under the present Gerrer Rebbe, Rabbi Yaakov Arye Alter. In 1999 the present rebbe asked Litzman to join the Aguda slate for the legislative election held that year. He has since served as the leader of the Agudat Yisrael faction in the Knesset, in which role he consults the Gerrer Rebbe on a daily basis. Litzman served on the Knesset's Internal Affairs Committee from 1999–2001, and as the Deputy Chairman of Knesset Labor and Welfare Committee.
As part of the coalition agreement with the ruling government of Ariel Sharon in 2001, Litzman was appointed chairman of the Knesset Finance Committee, a position he held until 2003, and again from 2005-2007. Litzman is quoted as saying that "in some respects, I envy the low profile the Haredi community in the United States has been able to retain by staying out of politics". He also said that, in Israel, the media attention makes for misrepresentation and misunderstanding of the Haredi community.
Following the 2009 elections in which Litzman retained his Knesset seat, his party joined the newly established government of Prime Minister Benjamin Netanyahu. He was appointed Minister of Health. Litzman retained his position as Minister of Health following the 2015 elections.
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