2010 marks the 20th anniversary of the death of Dunbar, who wrote honestly about her upbringing on the Buttershaw Estate and was hailed as "a genius straight from the slums" by playwright Shelagh Delaney.
Her first play, The Arbor, originally written as part of a school assignment, described the experiences of a pregnant teenager with an abusive, drunken father.
Its success at The Royal Court Theatre led to her commission to write Rita Sue and Bob Too in 1982. The play and subsequent film by Alan Clark, was described as "Thatcher's Britain with its knickers down."
The film garnered critical acclaim at the Cannes, Berlin and Edinburgh Film Festivals in 1987 and is now considered a cult classic.
The unveiling was followed by special screening of The Arbor, a powerful new film at Pictureville, National Media Museum. The Arbor will open in cinemas nationwide from Friday.
Tony Earnshaw, head of film programming at the National Media Museum said: "Andrea Dunbar and her works represent an extremely important part of the cultural landscape in Bradford.
"Andrea died tragically young before she was able to further realise her tremendous gifts. To have a plaque unveiled in her memory, alongside the first screening of this new film in her home city, is a worthy and fitting tribute to that talent."
Dunbar died aged 29 in 1990, leaving 10-year-old daughter Lorraine with bitter memories.
The Arbor catches up with Lorraine in the present day, also aged 29, and in prison undergoing rehab. Reintroduced to her mother's plays and letters, the film follows Lorraine's personal journey as she begins to understand her mother's struggles.