In 1940, Melhase was an undergraduate in the college of chemistry at the University of California, Berkeley. She was president of the Student Affiliates of the American Chemical Society and was considering doctoral studies and a career in chemistry. Honors students typically took on research projects at the time, and she sought advice from her close friend, nuclear chemist Gerhart Friedlander; Friedlander was then a graduate student under the supervision of Glenn T. Seaborg, and he suggested she approach him for a project. She spoke to Seaborg in his lab, and he proposed they work together to search for a Group 1 element among the fission products of uranium. Her laboratory was above those of Nobel Prize winners Willard Libby and Melvin Calvin.
In March 1941, Melhase worked with Art Wahl. He handed her 100 grams of a uranium compound (uranyl nitrate) that had been neutron-irradiated by a cyclotron. Using a Lauritzen quartz fiber electroscope, she discovered the Cs-137 several months later. Despite establishing herself as a promising young experimental scientist, nuclear research during World War II was treated with strict secrecy and it was not publicized. Significant research on the isotope followed, but their results were not made available until after the war.
Melhase received a bachelor's degree in nuclear chemistry and planned to apply for graduate studies at UC Berkeley. However, the head of the chemistry department, Gilbert N. Lewis, was refusing entry to women; the last woman the department admitted had gotten married shortly after her graduation and he considered her education a "waste". She worked for the Philadelphia Quartz Company in El Cerrito, California. She rejoined the Manhattan Project from 1944 to 1946. Without an advanced degree, she did not continue her career in science.
Though references to her work are scant, Seaborg shares credit of his discovery of Cs-137 with her. Writing in 1961, he stated:
He also wrote in 1990 that "it is appropriate to credit both G. T. Seaborg and M. Melhase for the birth of cesium 137."