Kaj Hansen only measured 166 cm, and was affectionately known as "Lille Kaj". He had excellent technique, balance and dribbling skills, and could play in all attacking positions apart from centre forward. He played the bulk of his career with Boldklubben af 1893. Hansen made his senior debut with B 93 in 1934, and won the Danish football championship with the club in 1934 and 1935. Hansen made his debut for the Denmark national football team on 30 June 1936, scoring one goal as the Norway national football team was defeated 4–1. In 1939, he scored two goals as Denmark won the 50-year anniversary tournament of the Danish Football Association, and was named player of the tournament. Hansen won an additional Danish championship with B 93 in 1939. As an unpaid amateur player, Hansen was free to move between clubs. He had a brief stint with B 93's rival club Boldklubben Frem from August to November 1940, scoring four goals in five games with the team. He moved back to B 93, with whom he won the 1942 and 1946 Danish championships. In September 1945, Kaj Hansen took part in a game of regional select teams played in Aarhus, alongside fellow Danish internationals Arne Sørensen, Børge Mathiesen, Kaj Christiansen, and Egon Sørensen. They were all subsequently banned for the rest of the year by both the Danish Football Association and the Copenhagen Football Association for excessive drinking on the trip. In 1946, Kaj Hansen and Arne Sørensen both accepted payment to play for Skovshoved IF, in violation of the amateur-only code of the Danish Football Association. They were declared professionals, which barred them from playing football for both Danish clubs and the Danish national team. Hansen and Sørensen moved abroad to continue playing professionally, and they joined Stade Francais. Here they played alongside Børge Mathiesen. The physical side of the professional game did not suit Kaj Hansen, who spent much of his professional career out with injury. He represented French teams Stade Francais, SR Colmar, FC Metz, and CA Paris, before ending his playing career in 1950. Kaj Hansen became a popular manager of several Danish teams. He went on to manage Randers Freja, Vejle Boldklub, Odense Boldklub, and B 1909. He also managed the Danish second-string national team for five unofficial games in 1958 and 1960, winning two games and losing one.
Honours
Danish football championship: 1934, 1935, 1939, 1942, 1946
Danish football championship, top goalscorer: 1940