The 79-year-old actor had been battling chronic kidney disease
, local media reported. His death was confirmed by Dr. Ram Narain, executive director at the Kokilaben Hospital.
Kapoor won immense popularity for his roles in Hindi films including "Jab jab Phool Khile" (When a Flower Blossoms), "Awara" (Vagabond), and "Kabhi Kabhie" (Sometimes), as well as his good looks.
Bollywood fans shared their memories and favorite pieces of Kapoor dialogue on social media Monday. Many described his death as the end of an era.
India's Prime Minister Narendra Modi was one of those to offer his condolences, tweeting:
"Shashi Kapoor's versatility could be seen in his movies as well as in theatre, which he promoted with great passion. His brilliant acting will be remembered for generations to come. Saddened by his demise. Condolences to his family and admirers."
Kapoor was born into a movie family. His father was an actor and playwright, performing all over the country during the Partition era with his repertory company the Prithvi Theaters. Kapoor's father starred in the plays which touched on the plight of refugees, nationhood, and the country's trajectory.
While Kapoor did play the stereotypical romantic Bollywood hero in many films, he did it out of compulsion to take care of his family, said Aseem Chhabra, author of "Shashi Kapoor: The Householder, the Star."
The actor's real passion was theater. In 1972, Kapoor and his wife, Jennifer Kendal, founded the Prithvi Theatre
in Mumbai. Its establishment was a dream of Kapoor's father.
Today the theater continues putting on plays in Hindi, English, Gujarati and Marathi.
Kapoor also acted in art films. He worked with Merchant Ivory Productions and later produced films of his own that were dedicated to social realism -- a far cry from the glitzy song and dance numbers of Bollywood.
Kapoor 'devastated' by wife's death
His career and life took a turn after the death of his wife in 1984, according to Chhabra.
Kapoor stopped acting for the most part and took up drinking instead, Chhabra said. He was drinking up to a bottle of vodka per day, at times. "He was devastated."
But for his fans, he will be remembered as the romantic, good-looking hero who could act alongside anyone.
Perhaps his most famous piece of dialogue comes from his role in the film "Deewar" (Wall). The story has him playing opposite one of Bollywood's biggest actors Amitabh Bachchan. The two play brothers in the film. Kapoor who becomes a police officer, is foil to Bachchan's character, who becomes a gangster in the city of Mumbai.
At the end of the film, the two brothers confront each other. Bachchan's character tells Kapoor, he has wealth, he has everything and asks him what he (Kapoor) has. Kapoor's response "Mere pas maan hai,"(I have mom) stuns Bachchan into silence.