Malinowski was born in Nowe to a Polish father Anastazy Malinowski, and a Scottish mother, Irene Malinowska (née Dowell). He was named after the famous anthropologist. Throughout most of his career he competed for Olimpia Grudziądz. His first international medal was the 2000 metres steeplechase gold at the 1970 European Junior Championships. In his first major senior competition, the 1971 European Championships, he broke the national 5000 metres record which was enough for the eighth place.