Mildred was born Mildred Spiewak on November 11, 1930, in Brooklyn, the daughter of Ethel (Teichtheil) and Meyer Spiewak, who were Polish Jewish immigrants.
Raised in the Bronx, Dresselhaus received her high school degree at Hunter College High School. She received her undergraduate degree at Hunter College in New York in 1951, and was counseled by future Nobel-Prize-winner Rosalyn Yalow to pursue further education in physics. She carried out postgraduate study at the University of Cambridge on a Fulbright Fellowship and Harvard University, where she received her MA from Radcliffe College. She received a PhD from the University of Chicago in 1958 where she studied under Nobel laureate Enrico Fermi. She then spent two years at Cornell University as a postdoc before moving to Lincoln Lab as a staff member.
Dresselhaus had a 57-year career at the Massachusetts Institute of Technology. She became a visiting professor of electrical engineering at MIT in 1967, became a tenured faculty member in 1968, and became a professor of physics in 1983. In 1985, she was appointed the first female Institute Professor at MIT
Dresselhaus was awarded the National Medal of Science in 1990 in recognition of her work on electronic properties of materials as well as expanding the opportunities of women in science and engineering. And in 2005 she was awarded the 11th Annual Heinz Award in the category of Technology, the Economy and Employment. In 2008 she was awarded the Oersted Medal, and in 2015 the IEEE Medal of Honor.
In 2000–2001, she was the director of the Office of Science at the U.S. Department of Energy. From 2003 to 2008, she was the chair of the governing board of the American Institute of Physics. She also has served as president of the American Physical Society, the first female president of the American Association for the Advancement of Science, and treasurer of the National Academy of Sciences. Dresselhaus devoted a great deal of time to supporting efforts to promote increased participation of women in physics. In 1971, Dresselhaus and a colleague organized the first Women’s Forum at MIT as a seminar exploring the roles of women in science and engineering.