The toned down version of the game, which was revealed last week, will not be released in the UK or any other territories, reports Eurogamer.
Heavy Rain Edition Modifiée will be released later this month, and features "realistic-looking violence", downgraded from "extreme violence" - making it suitable for players aged 16 and over.
The original carried a PEGI 18 certificate, and featured scenes of "violence towards defenceless people".
Heavy Rain was released for PlayStation 3 in February 2010, selling more than one million copies in its first three months. A Move-enhanced edition of the game followed in October.
Earlier this year, Quantic Dream boss David Cage downplayed rumours that the studio is planning to release a sequel to the title.
Watch the announcement trailer below: