Born in Aarberg, Switzerland, Wüthrich was educated in chemistry, physics, and mathematics at the University of Berne before pursuing his Ph.D. under the direction of Silvio Fallab at the University of Basel, awarded in 1964. He continued post-doctoral work with Fallab for a short time before leaving to work at the University of California, Berkeley from 1965 to 1967 with Robert E. Connick. That was followed by a stint working with Robert G. Shulman at the Bell Telephone Laboratories in Murray Hill, New Jersey (1967-1969).
Wüthrich returned to Switzerland, to Zürich, in 1969, where he began his career there at the Eidgenössische Technische Hochschule (Federal Institute of Technology), rising to Professor of Biophysics by 1980.
He was awarded part of the Nobel Prize in Chemistry for his leadership of ongoing work, begun in the 1970s, on the use of multidimensional nuclear magnetic resonance spectroscopy to study the structure of proteins.