A veritable legend, Kumar acted in more than 65 films over nearly five decades, playing roles that ranged from the iconic to the endearing.
He was admitted to hospital on 30 June after he complained of breathlessness. He had been frequently ill for months.
Kumar is survived by his wife, Saira Banu, a Bollywood actress herself. The couple have no children.
His burial will take place at 17:00 local time (11:30 GMT). Maharashtra Chief Minister Uddhav Thackeray said the funeral would happen with state honours.
Mr Thackeray and several Bollywood stars, including Shah Rukh Khan and Ranbir Kapoor, visited Kumar’s family to pay their condolences.
Tributes have been pouring in on social media for the legendary actor – politicians, Bollywood stars and even historians have tweeted.
Dilip Kumar was born Yusuf Khan in December 1922 in Peshawar – in what is now Pakistan – before the partition of India.
Like some of his Muslim contemporaries, he took on a Hindu name – Dilip Kumar – when he joined the Hindi film industry.
He debuted in 1944 in Jwaar Bhata but it was the 1949 hit, Andaz, that shot him to fame. The blockbuster love triangle also starred Nargis and Raj Kapoor, who went on to become celebrated actors.
Kumar’s biographer Lord Meghnad Desai compares him to Hollywood great Marlon Brando or Italian legend Marcello Mastroianni.
“Dilip Kumar was arguably the best actor Indian cinema has produced. There are stars, some even bigger than him, but no better actor. He was the finest tragic actor of his days but also succeeded at comedy,” he told the BBC.
Kumar essayed a gamut of roles, including a villager, a suave urbanite, a Bengali gentleman and a swashbuckling hero, before moving to paying older, supporting roles in the 1970s, Mr Desai said.
“More than his list of films and his box office popularity, Dilip Kumar reflected India’s political and social evolution through his films,” he said. “As independent India grew, prospered, ran into difficulties and faced challenges, Dilip Kumar’s roles told the story as it unfolded.”
Kumar was honoured with prestigious film awards and two of India’s highest civilian awards.
He married Saira Banu in 1966 – the two starred together in several hit films. Kumar last appeared in a film in 1998.