Anfinsen was born in Monessen, Pennsylvania to a Norwegian American family. He earned a bachelor's degree from Swarthmore College in 1937, a master's degree in organic chemistry from the University of Pennsylvania in 1939, and in 1943 a Ph.D. in biochemistry from Harvard Medical School. While attending Swarthmore College he joined the Delta Upsilon Fraternity.
Anfinsen stayed at Harvard as an assistant professor until 1950, when he began working for the National Institute of Health, where he spent most of his career, until 1981. From 1982 until his death in 1995, Anfinsen was professor of biology at Johns Hopkins.
In 1961 he showed that ribonuclease could be refolded after denaturation while preserving enzyme activity, thereby suggesting that all the information required by protein to adopt its final conformation is encoded in its primary structure.