Nossal's family was from Vienna, Austria. He was born four weeks prematurely in Bad Ischl while his mother was on holiday. His family left their home town of Vienna for Australia in 1939 following Nazi Germany's annexation of Austria. As his father's grandparents were Jewish, he was also considered Jewish and at risk of being sent to concentration camps. In an interview with Adam Spencer, Nossal noted that his father was not a professing Jew but of Jewish ethnicity as he had been baptised a Roman Catholic as a child. Nossal remarked that his father "therefore thought that he would be somewhat protected from the Holocaust-type predicament. Of course, he hadn't properly read "Mein Kampf". It was all spelt out there: if your four grandparents were Jewish, then you were Jewish." He was baptised and remains a practising Roman Catholic.