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.
Ashok Singhal, a senior leader of India's Hindu nationalist Vishwa Hindu Parishad movement, has died aged 89.