The sale is included in the Islamic and Indian art auction scheduled for April 8 on New Bond Street, London.
Titled "Nalini", the painting is one of only three oil paintings by the artist ever to be offered at auction.
Procured from the artist's family, the artwork was previously exhibited in the Baghdad Fine Arts Institute in 1952, and was part of a travelling exhibition throughout India organised by the Iraqi government in 1955, where it was also published, the auctioneers said.
Mrinalini went on to gain international acclaim both for her performance and choreography. By her early twenties, Mrinalini had already performed in India, Europe and America with her company.
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"The present portrait was painted during her first London appearance in 1949 at St Martin's Theatre in London's West End with the "Ballets Hindous" which also performed in Geneva, Lucerne and Brussels in the same year," the auctioneers said.
At the time the portrait was painted Selim was studying in London on a government scholarship and mixing in artistic and musical circles where he met Mrinalini.
One of the founding fathers of Iraqi modernism, Jewad Selim was sent to Europe on government scholarships to further his art education, first to the Ecole des Beaux Arts in Paris (1938-39) and then to the Academia di Belli Arte in Rome (1939-40).