He was admitted to hospital near Delhi last Friday in a critical condition after complaining of breathlessness.
A leading figure in the drive to build a temple at a disputed religious site in Ayodhya, he was known for his anti-Muslim remarks. Ayodhya has sparked deadly riots and remains a flashpoint.
Prime Minister Narendra Modi described his death as "a deep personal loss".
Mr Singhal was the international president of Vishwa Hindu Parishad (VHP) - an affiliate of the Rashtriya Swayamsevak Sangh (RSS) - for more than 20 years. The VHP is a close ally of Mr Modi's ruling Bharatiya Janata Party.
"He passed away at 2.30pm today. He had multi-organ dysfunction, ARDS [acute respiratory distress syndrome] and sepsis and was being treated by a team of specialists," The Times of India quoted Dr AK Dubey of Medanta hospital in Gurgaon as saying.
The 16th Century Babri Masjid (mosque) was torn down in 1992, allegedly by activists of VHP and other hardline Hindu groups who claim the site is the birthplace of their deity, Ram.
Tributes have been pouring in for the controversial leader on Twitter. In a series of tweets, Mr Modi described him as "an institution":
Soon after the news of his death became public, Ashok Singhal began trending in India and was also the number two trend worldwide. Many tweets praised his role in "resurrecting" Hinduism in India, but not everyone shared that opinion.

Owner Tom Forrest also featured the phrase "man + woman = marriage" on the site for Cromasaig B&B in Kinlochewe.
The Equality and Human Rights Commission (EHRC) in Scotland had begun action to seek a court order.
However, it said this had been halted after Mr Forrest agreed to remove the phrases voluntarily.
The website said the guest house was "heterosexual friendly" and included a pictorial version of the statement "man + woman = marriage".
The commission said it was concerned that these phrases were potentially discriminatory.
It initially wrote to Mr Forrest asking for them to be removed after receiving complaints.
When no action was taken, the commission sought a court order which would require the phrases to be removed.
That legal action has been halted after the statements were deleted voluntarily.
Lynn Welsh, of the EHRC, said: "I am pleased that the owners of Cromasaig B&B have agreed to remove these phrases.
"Removing the phrases will have no negative impact on their business, and alleviates EHRC's concerns."
EHRC added that while the case had been "concluded successfully", the case raised questions surrounding the "continued prevalence of homophobic discrimination" which exists in Scotland.
Owner Mr Forrest sparked controversy in 2004 when he refused a gay couple a double room at the guest house.
The couple, from London, were told they could only book a twin room because their relationship was "unnatural".
As a result, the B&B had its recommended status removed by tourist authority VisitScotland.
Ashok Singhal, a senior leader of India's Hindu nationalist Vishwa Hindu Parishad movement, has died aged 89.
[NEXT_CONCEPT]
A Highlands bed and breakfast which was described as "heterosexual friendly" on its website has removed phrases after being threatened with legal action.