Entering the Vienna Music Academy at the age of 14, Streicher graduated in 1940 and spent the next four years serving as principal bass at the Kraków National Theater. In 1945 he joined the Vienna Philharmonic and spent 19 years (1954 - 1973) as principal. After 1966, Streicher devoted his time to instructing young students at the Vienna Musical Theater Academy and at the Escuela Superior de Música Reina Sofía (Queen Sofía College of Music) in Madrid.
After leaving the Vienna Philharmonic, Streicher contributed to the contrabass's development as a solo instrument. Performing solo, Streicher was able to showcase the expressive power of the instrument. As a soloist he recorded pieces ranging from Carl Ditters von Dittersdorf's 18th century compositions to contemporary contrabass pieces.