He passed away during treatment at the capital's Square Hospital at 9.10 am on Monday, his wife Sultana Rahman confirmed.
Babar had long been suffering from a combination of diabetes, blood pressure and lung ailments, she told bdnews24.com.
He was admitted to Square Hospital on Thursday after suffering a brain haemorrhage before his demise three days later.
Despite gaining recognition predominantly as a movie villain, Babar made his silver screen debut as a protagonist in the Amjad Hossain's 'Banglar Mukh'.
Babar also produced and directed a number of films, including 'Daiban' and 'Dagi'.
His body will be taken to the Film Development Corporation or FDC for a Namaz-e-Janaza after the Asr prayers, said Sultana. Babar will then be laid to rest at the Intellectuals' Graveyard in Mirpur in the evening.