Shubhangini Devi Gaekwad, wife of Puar's brother, the late Ranjitsinh Gaekwad, said Puar died after a brief illness. She had been admitted in a private hospital two days ago.
Prime Minister Narendra Modi condoled her demise through Twitter. "Mrunalini Devi Puar ji continued the Gaekwad family's glorious tradition of service through education, including as MSU Chancellor," Modi said.
Gujarat Chief Minister Anandiben Patel and BJP chief Amit Shah too expressed grief over Puar's death.
MSU was founded by erstwhile ruler of Baroda state, Sayajiirao Gaekwad-III in 1881. It is the only university in Gujarat where Chancellor is not the Governor of the state but a member of the former royal family.
Dr Puar was the first woman Chancellor of a recognised Indian University with more than 35,000 students.
She was also a member of the steering group on Nutrition, set up under the Planning Commission.