MUMBAI: Revered Bollywood actor Amitabh Bachchan's daughter-in-law and granddaughter have joined him and his son in testing positive for COVID-19, the family said on Sunday, in one of the highest-profile cases of the pandemic sweeping India.

From hospital with his father in Mumbai, Amitabh Bachchan's son Abhishek said his wife and former Miss World Aishwarya Rai Bachchan and their eight-year-old daughter had also been infected by the new coronavirus.

"Aishwarya and Aaradhya have also tested COVID-19 positive. They will be self quarantining at home," he tweeted, saying other family members had tested negative and thanking Indians for their wishes and prayers.

"My father and I remain in hospital till the doctors decide otherwise. Everyone please remain cautious and safe. Please follow all rules!" added Abhishek Bachchan, 44, also an actor.

He and his father were admitted on Saturday to hospital, where health officials said on Sunday they were stable.

Seventy-seven-year-old Amitabh Bachchan is one of India's most beloved personalities, and some fans were conducting Hindu prayer rituals for the whole family.

"It's shocking to know that one of the richest and most talented, educated family (sic) can get infected. We can only hope the family recovers as it's important for the morale of millions," tweeted one fan Jayant Sathe.

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The elder Bachchan had a near-fatal accident in 1982 when a table hit him in the abdomen while shooting a fight scene.

That triggered an outpouring of love, with one fan said to have walked backwards from southern Hyderabad city to Mumbai in his honour.

Aishwarya Bachchan, 46, who often features on "most beautiful" lists, has also worked in several Bollywood and Hollywood films. She is a brand ambassador for some multinational companies, including L'Oreal.