Between 1969 and 1984 he was capped 102 times for East Germany, scoring 55 goals. For a long time he was considered a member of the FIFA Century Club, but when FIFA changed regulations to no longer include games at the Olympic Games, four of his matches were deleted from his official FIFA record and he dropped out. The German Football Association still lists Streich with 102 caps on their website.
Streich is regarded as one of the best players for East Germany and holds both the records for most appearances and goals scored in the national team. Streich took part in the 1974 FIFA World Cup, scoring 2 goals in 4 matches.
During his career he played 378 games in the DDR-Oberliga for F.C. Hansa Rostock and 1. FC Magdeburg, scoring a record 229 goals. This tally earned him the top scorer award four times. He also scored 17 goals in 42 European matches for Rostock (4/0) and Magdeburg (38/17). In 1979 and 1983 he won the East German Footballer of the Year award. He also set the all-time DDR-Oberliga record for most goals scored in a game when he netted six in 1. FC Magdeburg's 10–2 defeat of BSG Chemie Böhlen in August 1977.