The eminent educationist was undergoing treatment for cardiological problems since last week, his family sources said.
Prof Barooah was admitted to hospital after he had complained of breathing problem and his condition had turned critical yesterday when he was put on ventilator support, the sources said.
A human rights activist, he had given guidance to the six-year-long anti-foreigners Assam Agitation in the early 80's culminating in the historic Assam accord in 1985.
In his condolence message Chief minister Tarun Gogoi said Barooah had immensely contributed to the social life of Assam through his writings, scholarship and contribution to the uplift of the education system in India.
Prof Barooah's son is prominent journalist Santanu Saikia whose wife Sabina Sehgal Saikia had died in the Mumbai terror attacks.