Vishnevskaya was born in Leningrad. She made her professional stage debut in 1944 singing operetta. After a year studying with Vera Nikolayevna Garina, she won a competition held by the Bolshoi Theatre in Moscow (with Rachmaninoff's song "O, Do Not Grieve" and Verdi's aria "O patria mia" from Aida) in 1952. The next year, she became a member of the Bolshoi Theatre.
On 9 May 1960, she made her first appearance in Sarajevo at the National Theatre, as Aida. In 1961, she made her Metropolitan Opera debut as Aida; the following year she made her debut at the Royal Opera House with the same role. For her La Scala debut in 1964, she sang Liù in Turandot, opposite Birgit Nilsson and Franco Corelli.