Mr Mukherjee had emergency surgery for a blood clot in his brain on August 10 at New Delhi’s Army Hospital Research and Referral.
The hospital said he tested positive for Covid-19 after the surgery and his condition was critical. He remained in a coma after the surgery.
The hospital said his health began declining on Monday after a lung infection resulted in septic shock.
His son, a former MP in India Abhijeet Mukherjee, tweeted in the evening that he had died.
Mr Mukherjee was president from 2012 to 2017, during a long period when the Congress party held power. The office is largely ceremonial in India, with executive powers resting with the prime minister.
Before that, he had been finance, defence and foreign minister for three separate prime ministers and helped manage their fractious governing coalitions.
