He is survived by his wife Subhadra and two daughters.
Lucknow-born Nehru was a three-time Lok Sabha member.
A columnist and psephologist, Nehru was admitted at a Gurgaon hospital for the past few weeks. Congress chief Sonia Gandhi and her daughter Priyanka Vadra paid him a visit recently and wished his speedy recovery.
Nehru, a key political figure of the Rajiv Gandhi era, had advised Rajiv Gandhi to field popular figures like Amitabh Bachchan, Sunil Dutt and Madhav Rao Scindia in the 1984 general polls. The former minister in charge of internal security, however, had a split with Gandhi subsequently and had joined hands with VP Singh who had formed the Jan Morcha.
Janata Dal (U) leader Sharad Yadav described Arun Nehru as a "leader with political maturity" who played a key role in formation of the Janata Dal government.
Nehru's funeral will take place at the Lodhi crematorium in New Delhi on Friday.