The Congress party leader of West Bengal had been in coma for nine years. Doctors pronounced him dead on Monday.
Known as 'Priya' in West Bengal's political circle, he had been information and broadcasting minister.
Hasina expressed 'deep condolence' over the demise of Priya Ranjan, according to the press wing of the Prime Minister's Office.
She also extended sympathy to the bereaving family.
The late leader's wife Dipa Dasmunsi was also a politician and had been elected to the Lok Sabha.
The prime minister remembered the role Priya Ranjan Dasmunsi played during the Liberation War in 1971.
Bangladesh has honoured him with 'Friend of Liberation War' award. His family received the award on his behalf in 2013.
Information Minister Hasanul Inu has also expressed condolence over his passing.