She is the only child of her parents. She was not formally trained in music; yet she went on to become a successful singing actress. She attended New Girls' school also known as J.B. Petit High School for Girls, in Fort, Bombay (Mumbai). She received religious teachings in Persian at home.

Music director Naushad once heard Suraiya's voice on All India Radio where she sang for a children's program, and chose her to sing as a 13 year old for Mehtaab in Kardar's film Sharda (1942).
In her adult she initially played secondary roles in K. Asif's Phool (1944), Anmol Ghadi (1946) and Dard (1947). She got a break as a heroine for the film Tadbir in 1945 at the recommendation of K. Asif's Phool, who liked her voice during a rehearsal. She went on to costar with Saigal in Omar Khayyam and Parwana.
Suraiya was romantically involved with actor Dev Anand. The two of them costarred in six films between 1948 and 1951. During the shooting of a film, a boat capsized and Dev Anand saved Suraiya from drowning. She fell in love with him, but her grandmother opposed the relationship. Suraiya remained unmarried all her life.