Grasselli Brown attended Harvey Rice Elementary School, Alexander Hamilton Junior High and John Adams High School in Cleveland, Ohio. At John Adams, she was in a college track program and planned to major in English in college. However, when she took her first chemistry class, she fell in love with the subject. Her high school chemistry teacher told her if she majored in chemistry, he would be able to get her a scholarship to his alma mater, Ohio University, which he did.
Grasselli Brown graduated from John Adams High School in 1946, and attended Ohio University from 1946 to 1950. She worked in the chemistry department as an assistant and in the library. She was a member of Phi Beta Kappa. She was the only female chemist in her class and received her Bachelor of Science summa cum laude in 1950. In 1958, she received her Master of Science in chemistry from Case Western Reserve University.
Grasselli Brown has received thirteen honorary degrees from various institutions including Ohio University (1978), Clarkson University (1986), Michigan Technology University (1989), Wilson College (1994), Case Western Reserve University (1995), Notre Dame College (1995), Kenyon College (1995), Mount Union College (1996), Cleveland State University (2000), Kent State University (2000), Ursuline College (2001), Youngstown State University (2003), and University Pecs, Hungary (2002).