Rai's father-in-law Amitabh Bachchan, 77, and her husband Abhishek Bachchan, 44, also major Bollywood celebrities, were admitted to Mumbai's Nanavati Hospital early this week, the highest-profile patients in India's epidemic of Covid-19.
Aishwarya Rai, a former Miss World and star of Hollywood film Bride & Prejudice, and her eight-year-old daughter, Aaradhya Bachchan had been in home quarantine.
The Times of India said they had been admitted to the top private hospital on Friday.
The Indian Express newspaper, citing the news agency PTI, said the family were responding well to treatment.
"They all are ok. Amitabh Bachchan and Abhishek Bachchan will be in the hospital maybe for a day or two,” said a hospital source quoted in the report.
Spokeswomen for Aishwarya Rai and the Nanavati Hospital did not respond to requests for comment.
Aishwarya Rai, 46, has worked on several Bollywood and Hollywood films and is a brand ambassador for multinational companies including L'Oreal.
India has registered over a million coronavirus cases, the world's third-highest number, and more than 26,000 people have died of Covid-19. Partial lockdowns have been re-imposed in some densely populated areas to control the spread of the virus.
