He says all required authorities, family members and staff have been informed of this and are all being tested.
Reacting to the news, actor Rajkummar Rao tweeted: "Prayers sir!"
US COVID-19 cases surpass 3 mln -- Johns Hopkins University
Around the world, almost 12 million people have contracted the virus and about 540,000 have died. A number of states and cities have also introduced ordinances requiring masks in public places .
Amitabh also urged all those who have been in close proximity with him in the last 10 days to get themselves tested. The two actors, who live with their celebrity wives Jaya and Aishwariya Rai Bachchan, were recently diagnosed with COVID-19.
He, and Abhishek, 44, have been taken to Nanavati Hospital in Mumbai.
Abhishek too announced his Covid-positive status via a tweet. "I request all to stay calm and not panic", he added.
Coronavirus crisis: Victorian Premier Daniel Andrews announces 288 new COVID-19 cases
Currently, South Australia's border is all but closed to Victoria, with non-essential travellers not permitted to cross. The lockdown led the government to announce a half-a-billion-dollar stimulus package for affected businesses.
Amitabh Bachchan is one of the most admired stars in Bollywood, having appeared in some 200 films during his impressive 50-year-long career.
Actors and other Bollywood colleagues have tweeted their wishes for his quick recovery.
"Sending you tons of love and best wishes. please take care. you ll be okay very soon!", wrote Neha Dhupia. Today, Big B shared on his Twitter page that he has tested positive. His films still open to packed cinemas across India, but his new movie - comedy-drama "Gulabo Sitabo" - was released on Amazon's streaming service due to the coronavirus restrictions.
Florida's Walt Disney World to reopen
Nearly all of the shows that are normally performed are suspended and character meet-and-greets have been stopped. Visitors and employees will have to wear masks and undergo temperature checks before entering the parks.
He embraced social media, engaging with fans using Twitter and Tumblr and served as host of "Kaun Banega Crorepati", India's version of "Who Wants To Be A Millionaire".