Gorshin was born on April 5, 1933, in Pittsburgh, Pennsylvania, the son of Catholic parents Frances, a seamstress, and Frank Gorshin Sr., a railroad worker. He was of Slovenian ancestry. His father, Frank Sr., was a second-generation Slovenian-American whose parents emigrated to America from Slovenia. His mother, Frances or Fanny, née Prešeren, came to the United States as a young girl from Regrča Vas, near Novo Mesto, the main city of Lower Carniola, in Slovenia. Both of his parents were active in Pittsburgh's Slovenian community. They sang in the Slovenian Singing Society Prešeren, named after the great Slovenian poet France Prešeren. In an interview, Frances said that her son, being the product of a Slovenian home, spoke mostly Slovene before going to school. At the age of 15, he took a part-time job as a cinema usher at the Sheridan Square Theatre. He memorized the mannerisms of the screen stars he saw and created an impressionist act. He was still in high school when he obtained his first paid employment, which he secured as the prize in a Pittsburgh talent contest in 1951: a one-week engagement at Jackie Heller's New York nightclub, Carousel. His parents insisted that he take the engagement, even though his 15-year-old brother had been hit by a car and killed just two nights before.
After graduation from Peabody High School, Gorshin attended the Carnegie Tech School of Drama (now known as Carnegie Mellon University) in Pittsburgh. When not studying, he worked in local plays and nightclubs.
In 1953, Gorshin was drafted into the United States Army and posted to Germany. He served for a year and a half as an entertainer attached to Special Services. While in the Army, Gorshin met Maurice Bergman, who later introduced him to Hollywood agent Paul Kohner. Gorshin's Army service record was later destroyed in the U.S. National Personnel Records Center fire of 1973.