Born in 1917 in Vienna, Austria-Hungary, Munk was sent to a boys’ preparatory school in upper New York state in 1932. The family selected New York because they envisioned a career in finance for Munk in a New York bank with connections to the family business. His father, Dr. Hans Munk, and his mother, Rega Brunner, divorced when Munk was a child. His maternal grandfather was a prominent banker and Austrian politician, Lucian Brunner (1850–1914). His stepfather, Dr. Rudolf Engelsberg, was briefly a member of the Austrian government of President Engelbert Dollfuss.
Munk worked at the firm for three years and studied at Columbia University. He hated banking, and left the firm to attend the California Institute of Technology, where he earned a B.S. (1939) in physics. He applied for a summer job at the Scripps Institution of Oceanography in La Jolla, California. The next year the director of Scripps, the distinguished Norwegian oceanographer Harald Ulrik Sverdrup, accepted him as a doctoral student, but told Munk that he did “not know of a single job in oceanography which would become available in the next decade”.
Munk completed an M.S. in geophysics in 1940 and a PhD in oceanography from the University of California, Los Angeles, in 1947. After graduation, Scripps hired him as an assistant professor of geophysics. He became a full professor there in 1954.
In 1968 Munk became a member of JASON, a panel of scientists who advise the U.S. government.
On June 20, 1953, Munk married Judith Horton. She was an active participant at the Scripps Institution of Oceanography for decades, where she made major contributions to architecture, campus planning, and the renovation and reuse of historical buildings. Judith Munk died on May 19, 2006. Munk married La Jolla community leader Mary Coakley in June 2011.