Vishnevskaya was born in Leningrad, the town which is now called St Petersburg. In 1952 she won an important competition singing a song by Rachmaninoff and an aria by Verdi. She soon became a member of the famous Bolshoi Theatre in Moscow.
In 1960 she sang the part of in Aïda at the National Theatre in Sarajevo. In 1961, she made her first appearance at the Metropolitan Opera as Aïda and the next year she sang in the Royal Opera House in the same role. In 1964 she sang Aïda at La Scala.
Vishnevskaya was married to the cellist Mstislav Rostropovich from 1955 until his death in 2007. Her husband, as well as being a great cellist and conductor, was also an excellent pianist and he accompanied her for her recitals. They were very close friends of Shostakovich and Benjamin Britten and performed a lot of their works. She made many recordings including the main part in Shostakovich's opera Lady Macbeth of the Mtsensk District and in Britten's War Requiem. She had not been allowed to take part in the first performance of the War Requiem because the Soviet politicians would not let her sing together with the baritone Dietrich Fischer-Dieskau because he was German.
In 1974, they left the Soviet Union because they had criticized the Soviet government. They settled in the United States and Paris. In 1982 she retired from singing in opera. Her last role was in Paris where she sang Tatyana in Tchaikovsky's Eugene Onegin.
After the collapse of communism and the Soviet Union she and her husband were allowed to return from exile and live in Russia again. In 2002 she opened her own opera theater in Moscow: The Galina Vishnevskaya Opera Center.