Principal was born in Fukuoka, Japan, the eldest daughter of United States Air Force sergeant Victor Principal, after whom she was named and who was then stationed in Fukuoka. Her paternal grandparents were emigrants from Italy, originally surnamed Principale. Her mother, the former Bertha Ree Veal, was born in Georgia and was of English descent. Because her father was in the US military, they moved often; she grew up in London, Puerto Rico, Florida, Massachusetts, and Georgia, among other places. She attended 17 different schools, including studying at the Royal Academy of Ballet while her family was stationed in England.
She appeared in her first TV commercial aged five, and enjoyed a successful career in commercials. After graduating from South Dade Senior High School in 1968, she enrolled at Miami-Dade Community College, intending to study medicine. But months before completing her first year of studies, she was seriously injured in a car crash while driving home from the library. The other driver was convicted of drunk driving and served jail time. Principal spent months in recovery and was faced with the prospect of having to take her first year of studies over again. After a period of serious introspection, she drastically changed her life by moving to New York to pursue her acting career, and shortly thereafter to Europe. While living in London, she studied at the Royal Academy of Dramatic Art, and then in 1971, she moved to Los Angeles.