Balsai was born in Miskolc on 5 April 1947, the son of public prosecutor József Balsai (1915–1969) and teacher Mária Szalontai (1917–1991). His father participated in the Hungarian Revolution of 1956, as a result he was fired from his job and forced to work as a manual worker until his death. István Balsai finished his elementary and secondary studies in Budapest, where the family had lived since 1943. He earned a doctor of law at the Faculty of Law of the Eötvös Loránd University in 1972. He became a trainee lawyer in that year. He passed the special exam in 1974, and began to work for Budapest no. 21 Lawyer Working Community until the end of the Communist period. He worked as a private lawyer from 1995 to 2007.
