Veena was born as Tajour Sultana on 4 July 1926 in Quetta, Baluchistan Agency, British India.

Al Nasir was from a royal family in Bhopal and had already been married, first to actress Meena Shorey and then to Manorama.

She made her debut with Garib and Gawandhi (1942) at around sixteen years of age.

She played roles in big productions such as Halaku (1956), Chalti Ka Naam Gaadi (1958), Kaagaz Ke Phool (1959), Taj Mahal (1963), Do Raaste (1969) and Pakeezah (1972).

She retired in 1983 after the release of Razia Sultan (1983) in which she played Empress Shah Turkhan.