On Monday evening's News at Ten, two video clips were played as presenter Huw Edwards announced the Bollywood actor had died aged 79.
But neither of the men shown were Kapoor - one was his nephew Rishi and the other was actor Amitabh Bachchan.
The programme's editor Paul Royall apologised on Twitter for the mistake shortly after the bulletin aired.
But the error was criticised by some of the corporation's own stars on social media.
Adil Ray, the creator and co-writer of BBC One's Citizen Khan, tweeted: Someone at the BBC thought the brown person in this VT is the same person.
"Worse still, neither of them are the deceased actor Huw refers to. It's poor when it would have taken them seconds to verify. Not enough care."
Aasmah Mir, who presents Saturday Live on BBC Radio 4, said she was "really annoyed" by the error.
In a statement the BBC said: "BBC News at Ten is very sorry the wrong images were used to mark the death of Shashi Kapoor."
"The piece did not meet its usual standards and the programme has apologised for any upset."