Henkin was born in Pennsylvania in 1945 and raised in New Haven, Connecticut. His father was Dr. Avraham Hillel Henkin, who headed the local Board of Jewish Education. After graduating from the Yeshivah of Flatbush High School in 1962, he studied five years with his grandfather, Rabbi Yosef Eliyahu Henkin, from whom he received semichah. He also received semichah from Rabbi Yehuda Gershuni. During this time he also completed a master's degree in the sociology of religion at Columbia University. His uncle was Professor Louis Henkin, who taught international law at Columbia. He and his wife Chana Henkin moved to Israel in 1971 and he served as the Rabbi of the Beit She'an valley before moving to Jerusalem.