He joined up with Hamburg's youth team in 1970, then signed a professional contract in 1971. He remained there for thirteen seasons, making 568 league appearances. Along the way, he won domestic and European honors including one Bundesliga title (1979), one German Cup (1976), and the Cup Winners' Cup (1977).
Kaltz was active in the Hamburg attack, known in particular for his arcing right-footed crosses called "bananenflanken" ("banana crosses"). He also was a regular scorer--usually from the penalty spot--providing 76 goals. Unfortunately for Hamburg, however, he also set a Bundesliga record for own goals with six.
In 1989, he left Hamburg for a short spell in France with Bordeaux and FC Mulhouse, but returned in 1990 to play one last season with Hamburg before retiring in 1991. In all, he made a total of 581 league appearances, which places him second on the Bundesliga's all-time list behind Frankfurt's Karl-Heinz Körbel (602).