The not even 18 year old Schaub joined German Bundesliga side Eintracht Frankfurt at the beginning of the 1978/79 season. He should stay with the club until the winter break of the 1980/81 season. The promising talent never lived fully up to expectations and accumulated only 21 league matches for the "Eagles", in which he scored 3 goals. However, another goal engraved him forever in the club's history.
In 1980 Frankfurt faced off with league rivals Borussia Mönchengladbach in the all-German final of the UEFA Cup 1979/80. Frankfurt lost the first leg away 2-3. It was still 0-0 when in the 77th minute coach Friedel Rausch called Norbert Nachtweih, a highly respected player of his era, off the field and replaced him with the youngster. Only four minutes later Fred Schaub scored the only goal of the match and thus secured the only international title in the history of Eintracht.
From January 1981 until June 1983 he played in the second division for SpVgg Fürth, where he scored 36 goals in 84 matches, which was convincing enough for Borussia Dortmund to provide him with an opportunity for a comeback in the Bundesliga. He failed to distinguish himself and already in the winter break was passed back into the second division, this time to Hannover 96. There he became again part of the standard formation, which he even retained after the promotion to the Bundesliga in 1985, which may have been a sign for Hannover's resources being too thin. The club finished the season last, 10 points (2 points per win rule) away from a save place.
Schaub moved on to another second division club, SC Freiburg. There he featured in the regular line-up for the next two years.
With the beginning of the season 1988/89 Schaub chose to play in Austria. Initially he joined first division side FC Admira/Wacker in Vienna. There he impressed with his fighting spirit, and together with Gerhard Rodax and Walter Knaller he formed a highly memorable forward line. In his first season the club became runner-up in the championship and reached the cup final. In both cases Admira had to give in to the then mighty FC Tirol Innsbruck under the world champion of coaches Ernst Happel. Nevertheless, the club has not had a more successful year since. In the next season Schaub had his last European Cup campaign, this time in the Cup Winners' Cup, where later finalist RSC Anderlecht stopped Admira in the quarterfinals. In his time with the club Schaub scored 23 goals in 68 matches. In 1989 he was voted second best foreign player in Austria after his compatriot Hansi Müller.
After his time with Admira he spent some time with newly promoted VfB Mödling, second division side Favoritner AC and in the end at the amateur club USC Wampersdorf.
After his playing career Schaub remained in Austria and by 2003 worked as coach for the under 17s of VfB Admira Wacker Mödling, a club which was created in 1997 from a merger of his first two clubs in Austria..
Schaub died on 22 April 2003 after an accident on the autobahn near Fulda. On his way back to Austria from a visit at his mother his car crashed into a truck. His 8-year old son survived heavily injured.