Muñoz was born Marie Mounier in Van Nuys, California and then moved with her family to the Netherlands as a child. Rie and a sibling were returned to the US by their parents before the outbreak of World War II, where they lived with family friends. The parents intended to follow, but were unable to leave for seven years following the German invasion of the Netherlands. In the US, Muñoz studied art at Washington and Lee University. She visited Juneau, Alaska in 1951 as a visitor, but became enamored of Southeast Alaska and decided to stay.