His craft learned Stefan Huber at FC Unterstrass in Zurich. His career began when then Grasshopper Club Zurich in 1984. Due to its very quick, knee-jerk reactions, he was known to his friends and fans soon under the takeovers "Panther".
In 1988 he moved to Lausanne Sports, for whom he played for five years. In 1993 he signed with the former National League A- team FC Basel, where he played for six years. 1999 replaced the FC Basel Huber one at the Grasshopper against their former goalkeeper Pascal Zuber Buhler. Huber played until 2002 for the Grasshoppers and then there goalkeeping coach. He remained in this position until 2007.
Stefan Huber also played between 1991 and 1999 16 times for the Swiss national football team.