Heikki Ollikainen had a lengthy bandy career in his native Finland, playing for his local Oulu team. Between 1948 and 1964, he captured the Finnish national championship title six times (1953 and 1960–1964), was runner-up seven times (1948, 1950–1952, and 1957–1959), and came in third twice (1949 and 1954). On the international scene, he earned sixteen caps at various levels, including in the demonstration event at the 1952 Oslo Games, where Finland defeated Norway, lost against Sweden, and came in third due to goal differentials. Following his retirement, he coached both bandy and junior football. His brother Pentti was a two-time national ice hockey champion.