The pair were due to perform their second show at the venue, following on from last night's charity gig which was attended by Prince Harry.
The last-minute cancellation was explained on the venue's Twitter account.
"We're very sorry to say that tonight's concert has been cancelled due to Tony Bennett being taken ill. Apologies to disappointed fans," a message stated shortly after 8pm.
A follow-up added: "We will contact all ticket-holders as soon as we have any more information. We would also like to wish Tony a speedy recovery."
1/2 We're very sorry to say that tonight's concert has been cancelled due to Tony Bennett being taken ill. Apologies to disappointed fans.
— Royal Albert Hall (@RoyalAlbertHall) June 9, 2015
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Prince Harry was photographed with the singers yesterday, attending the show in his role as patron of children's charity WellChild.
The show saw the pair perform songs from their collaborative album Cheek to Cheek, accompanied by both a big band and an orchestra.
Watch Lady Gaga and Tony Bennett perform 'Bang Bang (My Baby Shot Me Down)' below:
