Kai Johansen began his football career in the small club of Korsløkke before moving to Boldklubben 1909 in Odense as a striker. However, he was not successful, and moved to another of the major clubs in the city, Odense Boldklub. Here he found his natural place as a right full back and soon attracted attention from the Danish national manager. Johansen made his debut as a member of the Danish national football team on June 11, 1962 against Hungary. The following year and a half he played 20 national matches.
After attracting international interest, Johansen was the first of a number of Scandinavian players signed by Greenock Morton in 1964. The following year, Johansen signed for Rangers on June 24, 1965 for £20,000 after impressing manager Scot Symon with his performance for a European Select side against a UK Select in Stanley Matthews' testimonial.
Johansen is best remembered for his goal in the 1966 Scottish Cup final. After a 0-0 draw against rivals Celtic, he scored a 25-yard goal to seal a 1-0 win for Rangers. He was the first ever foreign player to score in a Scottish Cup final. This cup victory earned Rangers qualification to the following season's Cup Winner's Cup and they reached the final for the second time in their history, only to lose against Bayern Munich. Johansen featured throughout the run to the final, including scoring a goal in the 2-1 first leg win against Borussia Dortmund, the holders, who Rangers knocked out of the tournament.
Becoming a professional footballer excluded Johansen from the national team, which at the time entirely consisted of amateurs. He undoubtedly would have had many more caps without this rule.
He retired in 1970 and returned to a career as a store owner. Before his career in Scotland, he had established a men's wear store in Odense. He also ran pubs in Glasgow and on the Costa del Sol, before becoming a player's agent.
He was diagnosed with cancer in 2006 and died on May 13, 2007. His death was marked with a minute's silence before Rangers' match against Kilmarnock that day.