Early years Brestrich began playing football for the youth teams of BFC Dynamo at eight years old and eventually went through all age groups at BFC Dynamo.
Playing career Brestrich joined the reserve team of BFC Dynamo in 1984. The team was coached by former professional player
Werner Voigt at the time. Brestrich made regular appearances for BFC Dynamo II in the 1984-85 DDR-Liga Nord. He was then allowed to finally make his debut for BFC Dynamo in the
DDR-Oberliga as a substitute for Olaf Hirsch in the match against
BSG Motor Suhl away on the 25th matchday of the
1984-85 DDR-Oberliga on 25 May 1985. BFC Dynamo won the match 8-0 and secured its seventh consecutive DDR-Oberliga title. Brestrich was registered in both the first team and reserve team for the 1985-86 season. He started the season as a regular player for BFC Dynamo II in the 1985-86 DDR-Liga Staffel A, but would then play for the first team in the DDR-Oberliga during the second half of
1985-86 DDR-Oberliga. Brestrich eventually became
East German champion with BFC Dynamo at the end of the 1985-86 season. He made 12 appearances in DDR-Oberliga and two appearances in the
FDGB-Pokal with the first team of BFC Dynamo in the 1985–86 season. Brestrich continued to play for BFC Dynamo II in the
DDR-Liga in the following seasons, but would also continue to make sporadic appearances with the first team of BFC Dynamo in the DDR-Oberliga. He made 19 appearances with the first team of BFC Dynamo in the DDR-Oberliga and the
FDGB-Pokal in total between 1985 and 1988. Instead, he returned to BFC Dynamo, now named FC Berlin, for the 1991-92 season. The match away against
Eisenhüttenstädter FC Stahl on the 13th matchday on 6 November 1999 would be his last appearance for the first team of BFC Dynamo. Brestrich was personally sacked by BFC Dynamo Club President Volkmar Wanski, who had sided with Coach Goldbach, and transferred to
VfB Leipzig. Bresicht has played in a total of 301 matches for BFC Dynamo during his career, including 282 matches between 1991 and 1999. Brestrich is very popular with the supporters of BFC Dynamo and has popularly been called "Heiko Brestrich - Football God" (). After retiring from his professional career, Brestrich has regularly appeared for the traditional team of BFC Dynamo. ==Honours==