Hans Heinemann began his amateur cycling career in the late 1950s, initially competing in road races. From 1960 Heinemann switched his focus to the track, finishing third in the individual pursuit at the Swiss national championship. That same year he was part the team pursuit that competed at the Roma Olympics. As a track specialist he won three individual pursuit titles at the national championships in the early 1960s. By 1964 Heinemann moved back to road cycling, riding in the road race at the Tokyo Olympics, as well as competing in the Milk Race in England.