Perry was raised on the west side of Chicago, where she graduated from Marshall High School. Her education continued at Howard University, where she was a member of the Howard Players under the direction of Owen Dodson. In 1950, she received a BA in drama from Howard. Her studies followed at the Goodman School of Drama at the Art Institute of Chicago (now at DePaul University), where she received an MFA in directing. She also grraduated from the Royal Academy of Dramatic Art in London in 1955.