Fink began his career with Borussia Dortmund's reserve squad before moving to SG Wattenscheid 09, where he helped them gain promotion to the first division of German football, the 1. Bundesliga, in 1990. After the club's relegation in 1994, he moved to Karlsruher SC, where he spent three seasons as a regular and impressed so much that he earned himself a move to the most successful club in Germany, Bayern Munich, in 1997. He subsequently spent seven seasons at Bayern, five of which as a regular, but lost his place in the starting lineup in 2002 and was transferred to the club's reserve squad in the German third division, the Regionalliga, in February 2003, although he managed a return to the Bundesliga squad in late April 2003. In the 2003–04 season, he became a regular in Bayern's reserve squad and only made one, his last, Bundesliga appearance that season, coming on as a substitute against VfL Wolfsburg in September 2003. His contract with Bayern's Bundesliga squad expired in June 2004 and he subsequently only continued to play another two seasons for the club's reserve squad before definitely ending his playing career upon the end of the 2005–06 season.