Swaraj died of a heart attack and was rushed to the emergency ward of All India Institute of Medical Science hospital, the Press Trust of India reported.
Swaraj was the external affairs minister in Prime Minister Narendra Modi's cabinet from 2014 to 2019. She distinguished herself with an active presence on social media, often replying to requests for help from Indians abroad.
After undergoing a kidney transplant during her tenure as minister, Swaraj decided not to run for this year's general election, citing health issues.
In a series of tweets, Modi said that Swaraj's death was a "personal loss" and that she had worked tirelessly at India's external affairs ministry.
Swaraj's last tweets thanked Modi for bringing a measure to Parliament to revoke constitutional protections for the disputed Himalayan territory of Kashmir. The bill lawmakers passed earlier Tuesday strips Jammu and Kashmir - India's only Muslim-majority state - of its statehood. The law also does away with the region's right to its own constitution and to Kashmiris' hereditary rights to land, jobs and scholarships.
Swaraj called it a "bold and historic decision."
"Thank you Prime Minister. Thank you very much. I was waiting to see this day in my lifetime," she wrote.
Opposition Congress party leader Rahul Gandhi described Swaraj as "an extraordinary political leader, a gifted orator and an exceptional parliamentarian with friendships across party lines."
Swaraj received a law degree and began her political career in the 1970s closely associated with socialist leaders. She actively opposed an emergency rule imposed in 1975 by then-Prime Minister Indira Gandhi of the Congress party. She later joined the Bharatiya Janata Party and rose to become one of its top leaders, last serving as India's foreign minister, only the second woman in the role after Indira Gandhi.
She was a member of the Haryana state legislature from 1977 to 1982 and again from 1987 to 1990. She then entered national politics and served as information and broadcasting minister, parliamentary affairs minister and health minister.
She also served as the chief minister of Delhi in the late 1990s.
Swaraj is survived by her husband, Swaraj Kaushal, a senior advocate of the Supreme Court of India and a former governor of Mizoram state, and a daughter, Bansuri, also an advocate.
J.P. Nadda, working president of the BJP, said Swaraj's body will be kept at the party office on Wednesday for people to pay homage and cremated later in the day.