Malez was born to a large family in the small town of Ivanec, in northwestern Croatia on 5 November 1924, at his family home. He was the first of six children of a local barber and amateur photographer Slavko Malez, and Matilda Malez (née Polak). He finished elementary school in 1939. In the summer of 1935, a local naturalist and archaeologist Stjepan Vuković organized an exhibition of prehistorical finds from Vindija Cave and Sever's quarry near Vuglovac, and this event in Malez's early childhood certainly affected his future career.
