Munk was elected to the National Academy of Sciences in 1956 and to the Royal Society of London in 1976. He has been both a Guggenheim Fellow (three times) and a Fulbright Fellow. He was also named California Scientist of the Year by the California Museum of Science and Industry in 1969. Among the many other awards and honors Munk has received are the Arthur L. Day Medal, from the Geological Society of America in 1965, the Sverdrup Gold Medal of the American Meteorological Society in 1966, the Gold Medal of the Royal Astronomical Society in 1968, the first Maurice Ewing Medal sponsored by the American Geophysical Union and the U.S. Navy in 1976, the Alexander Agassiz Medal of the National Academy of Sciences in 1977, the Captain Robert Dexter Conrad Award from the U.S. Navy in 1978, the National Medal of Science in 1983, the William Bowie Medal of the American Geophysical Union in 1989, the Vetlesen Prize in 1993, the Kyoto Prize in 1999, the first Prince Albert I Medal in 2001, and the Crafoord Prize of the Royal Swedish Academy of Sciences in 2010 “for his pioneering and fundamental contributions to our understanding of ocean circulation, tides and waves, and their role in the Earth’s dynamics”.
Munk gave the 1986 Bakerian Lecture at the Royal Society on the Acoustic monitoring of ocean gyres.
In 1993 Munk was the first recipient of the Walter Munk Award given “in Recognition of Distinguished Research in Oceanography Related to Sound and the Sea.” This award is given jointly by the Oceanography Society, the Office of Naval Research and the US Department of Defense Naval Oceanographic Office.