Born in Cologne, Kunde started his cycling career in 1959 as amateur.

His biggest success was in the 1966 Tour de France, where he wore the yellow jersey for five days.

Because he was relatively small (1.59 m or 5 ft 3 in, and 50 kg or 110 lb), Kunde was nicknamed Bergfloh and Karl, der Kurze (Karl the short).

The French reporters named him Le petit Kunde, and his concurrent Jacques Anquetil named him Mikrobe.

In 1973 Kunde ended his cycling career, and started a bicycle shop in Cologne.