Bachchan, 77, announced his diagnosis and hospitalization on Twitter, urging those who had been in close proximity to get tested.
His 44-year-old son, Abhishek, also announced Saturday that he has tested positive.
Bachchan is one of India's best known film actors and has been involved in 200 films since his career began in the 1970s.
He has enjoyed starring roles in hit movies including Zanjeer and Sholay, and has won four National Film Awards and 15 Filmfare Awards. He also had a brief cameo in Baz Luhrmann's 2013 adaptation of The Great Gatsby.
He is also a winner of the French Legion of Honor.
Bachchan also had a brief stint in politics, having been elected as a member of India's parliament. He resigned three years later, disillusioned by a corruption scandal under then-Prime Minister Rajiv Gandhi's government.