The Indian actress, a former Miss World and one of Bollywood's most famous faces, is being treated at Mumbai's Nanavati Hospital, ANI agency reports.
Her daughter Aaradhya has also been taken to hospital, PTI agency reports.
Aishwarya's husband Abhishek and father-in-law Amitabh Bachchan, both also famous actors, have been in hospital since Saturday with the virus.
On Sunday, 77-year-old Amitabh Bachchan - a Bollywood superstar who has achieved global fame during his long and illustrious career so far - tweeted that he had tested positive for the virus.
Another series of tweets from his son Abhishek, also a famous actor, confirmed that he, his 46-year-old wife Aishwarya and eight-year-old daughter Aaradhya had also tested positive.
Jaya Bachchan, also a famous actress and Amitabh Bachchan's wife, tested negative.
Until now Aishwarya Rai and Aaradhya have been isolating at home.
News that the family, often described as Bollywood royalty, had been affected by the coronavirus sent shockwaves across India. This week, thousands of fans have held prayers for the family's recovery.