Steinberg was born in 1947, in a displaced persons camp in Hof, Germany. With his parents he came to Israel at the age of 2 years.
Steinberg studied medicine in the Hebrew University-Hadassah Medical School and trained as a pediatrician and a pediatric neurologist in Jerusalem and in New York. He served in the air force of the IDF as a physician.
Steinberg was the first director of the Schlesinger Institute for Medico-Halakhic Research at the Shaare Zedek Medical Center, Jerusalem, and the founder and first editor of the quarterly "Assia" (in Hebrew) devoted to issues in medicine and Jewish law (halakhah).
He served as the Director of the Medical Ethics Center of the Hebrew University-Hadassah Medical School.
Steinberg published 36 books and public reports, and over 270 articles in the fields of Jewish medical ethics, general medical ethics, pediatric neurology and the history of medicine.
His major work is the 7-volume "Encyclopedia Hilchatit Refuit" (in Hebrew), which was translated into English by Fred Rosner "Encyclopedia of Jewish Medical Ethics" in 3 volumes.
Steinberg received many prizes, the most significant one - the Israel Prize in 1999.
Steinberg serves as an advisor in medical issues to the most prominent and authoritative Rabbis worldwide.
He also has served as chairman or member in many public committees, such as the Dying Patient Act, The Respiratory-Brain Death Act, Organ Transplantation Act, the Israeli National Bioethics Council, and others.
Currently, Steinberg is the director of the medical ethics unit & senior pediatric neurologist at the Shaare Zedek Medical Center, Jerusalem, Israel as well as the director of Yad Harav Herzog Institutes & head of the editorial board of the Talmudic Encyclopedia, Jerusalem, Israel, and co-chairman of the Israeli National Bioethics Council.