Zemach was born in 1886 in Płońsk, Poland, then part of the Russian Empire, and was a descendant of Rabbi Avraham Gombiner (known as the "Magen Avraham") and his descendant, Rabbi Zvi Hirsch HaLevi of Plonsk (known as the "Plant (Zemach) of Avraham", from where Zemach's surname originates). His family was the wealthiest in Płońsk.[1] He was a childhood friend of David Ben-Gurion. Zemach received a traditional Jewish education at cheder and beit midrash.