Asoke Nath Mitra was born on 15 April 1929, in Rajshahi, now in Bangladesh, to Jatindra Nath and Rama Rani Mitra. He married Anjali Mitra (née Ghosh) in November 1956. His father, Jatindra Nath Mitra, taught mathematics in Ramjas College, Delhi University. Mitra too went to Ramjas College to study mathematics, obtaining his bachelor's degree in 1947 and M.A. in 1949. He started his work in physics in 1949, as a Ph.D. student working with R. C. Majumdar.