She was born in Chicago, Illinois.
Tureck did not only play Bach's music, but had a wide ranging repertoire which included works by composers including Beethoven, Brahms, Chopin, and more modern composers such as David Diamond, Luigi Dalapiccola, and William Schuman. Diamond's piano sonata #1 was written because the composer was inspired by Tureck's playing.
For a while she followed Wanda Landowska in playing Bach's keyboard music on a harpsichord, but later on turned back to playing on the piano, and most of her later recordings are for the piano. She was an honorary fellow of St Hilda's College, Oxford.
She died in New York.