From a young age, Kenkhuis had a strong interest in swimming. In 1998, he won gold medals in both the 100 meter and 200 meter freestyle events in the European Junior Championships. At the 2000 Olympic Games in Sydney, Australia, Johan was a member of the bronze medal 4×200 meter freestyle relay team. He also helped the Netherlands win a silver medal at the FINA World Championships in Fukuoka, Japan in 2001 as a member of the 4×100 meter freestyle relay team.