The 84-year-old was in hospital to remove a clot in his brain when it was discovered he also had Covid-19.
Before serving as president between 2012 and 2017, Mr Mukherjee held several important portfolios during his 51-year political career.
These included the finance, foreign and defence ministries.
His son, Abhijit, confirmed the news in a Tweet.
Indian Prime Minister Narendra Modi praised Mr Mukherjee's contribution to the country, saying the former president had "left an indelible mark on the development trajectory of our nation".