Schippers was born in Kalamazoo, Michigan. He began playing piano at age 4. He attended the Curtis Institute and the Julliard School. He made his debut at the New York City Opera at age 21, and the Metropolitan Opera at 23. He conducted world premieres of now well known music by Gian Carlo Menotti and Samuel Barber. He conducted in all the major opera houses of the US and Europe, most notably the Metropolitan Opera and La Scala, and founded Italy's Spoleto festival with Menotti.
At one time he was named as one of the 100 most important men in America. He was a regular conductor with the New York Philharmonic and the Chicago Symphony Orchestra, and made recordings with them as well, but in 1970 he finally took a full time orchestral position with the Cincinnati Symphony Orchestra, succeeding his predecessor at the Metropolitan Opera, Max Rudolf. After making several recordings with them and building the orchestra's international reputation, his career was tragically cut short by his suddent death from lung cancer at age 47 in 1977. He made many opera recordings in his time, and live recordings of his performances are gradually being made available on CD.