He earned a Ph.D. in Theoretical Physics in 1981 from Stony Brook University (then called the State University of New York at Stony Brook). After spending two years at the International Centre for Theoretical Physics at Trieste, Italy, he returned to India where he has worked at the Tata Institute of Fundamental Research in Mumbai, India since 1984. In November, 2012 he joined Indian Institute of Science Education and Research, Pune as the head of physics department.
His major publications deal with fundamental properties of string theories, and include the conformal invariance of supersymmetric two-dimensional field theories which describe the world-sheet dynamics of strings, the study of supersymmetric solitons using index theorems, the discovery of a new duality between string theory and M-theory, the identification of string networks as supersymmetric states and the discovery of a novel Higgs mechanism in the worldvolume theory of M-theory membranes.
In 2002, he played a role in exposing a series of instances of plagiarism by the Vice-Chancellor of Kumaon University in India. The Vice-Chancellor was eventually found guilty by a national committee and subsequently resigned.
Mukhi has a number of interests in addition to physics, notably Indian Classical Music on which he maintains a webpage , science popularisation which he carries out through seminars at schools and colleges as well as newspaper articles, and cinema, cooking and meditation. Within the field of Indian Classical Music he has spent considerable effort archiving classic recordings, particularly those of notable vocal artist Pandit Kumar Gandharva on whom he also maintains a webpage . He also writes a blog, named "Tantu-jaal"
Mukhi is a Fellow of the Indian Academy of Sciences, Indian National Science Academy and The World Academy of Sciences, and a recipient of the S.S. Bhatnagar Award for Physical Sciences, 1999 and the J.C. Bose Fellowship, 2008. He has been an Editor of the Journal of High Energy Physics since its inception. He is Chair of the Panel on Scientific Values of the Indian Academy of Sciences and of the Ethics Committee of IISER Pune.
Mukhi was an invited speaker at the international conferences Strings 2000 in Michigan, Strings 2002 in Cambridge and Strings 2008 in Geneva. He was one of the organisers of Strings 2001 in Mumbai - a conference that attracted much publicity because of the participation of David Gross, Stephen Hawking and Edward Witten among other luminaries in the field. He has also lectured at advanced schools in theoretical physics, notably at Cargèse and Les Houches in France, at the SERC school series in India, and at the first PITP School at the Institute for Advanced Study in Princeton during his sabbatical year there.