Rabbi Avraham Shag (Schag-Zwebner) was born on 4 Iyar 5561 (1801) in Galgóc, Hungary (today Hlohovec, Slovakia). Orphaned of his father, Rabbi Yehuda Leib Shag, at the age of three, he was entrusted by his mother to Rabbi Yitzchak Frankel, rabbi of Regensdorf, who raised him. According to family tradition, the name "Shag" comes from the verse "The lion has roared (shaag), who will not fear?", which the Noda BiYehuda had written on his father's semicha.

Before his bar mitzvah he was sent to the Chatam Sofer's yeshiva in Pressburg, where he received semicha; his teacher called him "a gaon and a tzaddik". At eighteen he married the orphaned daughter of Rabbi Aharon HaLevi Spitz, av beit din of Prossnitz: the Chatam Sofer, who had chosen him as the finest student of his yeshiva, stood on the groom's side and Rabbi Mordechai Banet on the bride's.

He first inherited his father-in-law's rabbinic post, then, before the age of twenty-five, became rabbi of Schattmannsdorf, where he opened a yeshiva, and finally of Kobersdorf, one of the Seven Communities of Burgenland, which he led for twenty-five years while heading a yeshiva attended by many students. Like his teacher, the Vilna Gaon and the Baal Shem Tov, he held Jerusalem at the centre of his concerns, and at the end of his life he fulfilled his dream and settled there.

He passed away in Jerusalem on 29 Adar 5636 (1876) and rests on the Mount of Olives.