Khan, aged 54, was battling a rare form of cancer and died at a hospital in the city of Mumbai.
The late actor played memorable roles in the movies such as ‘Life of Pi’, based on the novel by Canadian author Yann Martel, and ‘Slumdog Millionaire’.
Famous actor Kamal Haasan described Khan as "one of the finest actors" whose work "always left me in awe."
Movie director, Shoojit Sircar, who made the film ‘Piku’ with Khan in a prominent role, wrote in a tweet: "You fought and fought and fought. I will always be proud of you."
Khan was born in the state of Rajasthan in a family with no connection to Bollywood.
"I am saddened and shocked to know about the untimely demise of one of our country's most versatile actors, Irrfan Khan. My heartfelt condolences to his family, friends and fans," Rajasthan Chief Minister Ashok Gehlot said.
The actor was diagnosed with a neuroendocrine tumour in 2018.
He is survived by his wife and two children.