Jenő Rácz was born on 18 July 1953, the son of teaching parents. He attended primary school in Felsőbogát and in Toponár. From 1967 until 1971 he attended Táncsics Mihály Grammar School in Kaposvár, where he was awarded a distinction on completion of school. In 1971 he won a place at Pécs University of Medicine, where he received a degree in medicine with honours in 1977. 

In 1977 he started work at Kaposvár Hospital, having been awarded a county scholarship. Two years later he asked to be transferred to Nagyatád Hospital, where he qualified as a surgeon in 1982. He then returned to Kaposvár Hospital and worked in the Accident Surgery Department, where two years later he qualified as an accident surgeon. Having specialised in arthroscopy, he led the department's arthroscopic team, working in the department until 1995. Latterly, he headed the hospital's operating block as chief surgeon and served on the hospital board of directors. 

From 1989 until 1993, he was a member of the chairmanship of Somogy County Wrestling Association, and from 1993 until 1994 he chaired the Medical Committee of the Hungarian Professional Boxing Association.  

In 1994 he received a diploma in Applied Management from the Healthcare Management Foundation. In 1995 he was awarded a second degree in Health Economics by the University of Economics. 

In 1995-96 Jenő Rácz headed the Organisation Department of the Ministry of Welfare, and between 1996 and 2002 he served as Managing Director of Kalocsa Municipal Hospital. While in that post he was elected for two terms as a member of the chairmanship of the Association of Hungarian Hospitals, where he chaired the IT Committee and the Debt Consolidation Working Group.  

In 2002 he was appointed as deputy state secretary in the Ministry of Health, Social and Family Affairs, a position he held until his ministerial appointment.  

Jenő Rácz is married to his second wife. He has four children, two of whom are adults with their own families.