The Indian Academy of Sciences elected Singh as a fellow in 1970 and the Council of Scientific and Industrial Research awarded him the Shanti Swarup Bhatnagar Prize, one of the highest Indian science awards in 1973. He became an elected fellow of the Indian National Science Academy in 1975 and four years later, the university Grants Commission of India selected him for the 1979 Meghnad Saha Award. He received the fellowship of the National Academy of Sciences, India in 1989 and the Goyal Prize for Physical Sciences in 1995. The Indian Science Congress Association awarded him the C. V. Raman Birth Centenary Gold Medal in 1996 and The World Academy of Sciences elected him as their fellow in 1999. He is also a fellow of the Institute of Physics and the award orations delivered by him include K. R. Ramanathan Memorial Lecture of Physical Research Laboratory (1995), Bicentennial Lecture of Indian Institute of Astrophysics (1995), S. N. Bose Memorial Lecture of S.N. Bose National Centre for Basic Sciences (1995), S. N. Bose Memorial Lecture of Kolkata Mathematical Society (1995), Meghnad Saha Lecture of National Academy of Sciences, India (1996) and Bhabha Memorial Lecture of the Institution of Electronics and Telecommunication Engineers (1997).
