Known to family, friends and colleagues as "Joey", Silverstein was born in Detroit. As a youth, Silverstein studied with his father, Bernard Silverstein, who was a public school music teacher. He began studies at the Curtis Institute of Music at age 12. His teachers included Efrem Zimbalist, D.C. Dounis, William Primrose, Josef Gingold, and Mischa Mischakoff. Although he never formally completed his high school education, Silverstein did graduate from Curtis in 1950. Following completion of his studies at Curtis, Silverstein played as a section musician with the Houston Symphony Orchestra, the Philadelphia Orchestra, and the Denver Symphony Orchestra.
In 1955, Silverstein joined the second violin section of Boston Symphony Orchestra (BSO), the youngest musician in the orchestra at the time. In 1959, he won a silver medal at the Queen Elisabeth Music Competition, and in 1960 he won the Naumburg Award from the Walter W. Naumburg Foundation. In 1962, Silverstein became BSO concertmaster, a position he held for 22 years. He was appointed assistant conductor of the BSO in 1971. Whilst in Boston, Silverstein performed with other local ensembles such as the Civic Symphony and Banchetto Musicale. He also taught at the New England Conservatory, Yale University, and Boston University as well as serving on the faculty of the Tanglewood Music Center. Silverstein left the BSO in 1984.
Silverstein was music director of the Utah Symphony from 1983 to 1998. He served as acting music director of the Florida Philharmonic Orchestra in 2001 until the orchestra's demise in 2003. He was the artistic advisor to the Portland Symphony Orchestra for the 2007-2008 season. In addition to teaching in Boston, he served as a professor of violin at the Curtis Institute of Music. In 1969, he became a faculty artist at the Sarasota Music Festival. Silverstein performed on a 1742 Guarneri del Gesù.
Silverstein married Adrienne Shufro in 1954. They had two daughters and a son. His widow, children, and four grandchildren survived him.
- David Allen (2015-11-28). "Silverstein, Longtime Boston Symphony Orchestra Concertmaster, Dies at 83". New York Times. Retrieved 2015-11-28.
- Jeremy Eichler (2015-11-24). "Joseph Silverstein, 83; renowned violinist, BSO concertmaster". Boston Globe. Retrieved 2015-11-26.
- Michael McFall (2015-11-22). "Joseph Silverstein, a true maestro and former Utah Symphony conductor, dies". Salt Lake Tribune. Retrieved 2015-11-22.
- Andrew L Pincus (2015-11-23). "Former BSO concertmaster Joseph Silverstein dies". Berkshire Eagle. Retrieved 2015-11-22.
- Susan Rife (2015-11-23). "Joseph Silverstein was a musical force to be reckoned with". Sarasota Herald Tribune. Retrieved 2015-11-26.