His image of her behind bars depicts the last bar as a pencil, and next to the mural is a call for her release.
Dogan was jailed for two years and nine months last year in Turkey, for her painting of the Kurdish town Nusaybin.
Her picture, copied from a newspaper photograph, showed the town reduced to rubble during conflict.
The photograph was taken by government forces in the area where they had fought Kurdish militants.
It features Turkish flags draped over destroyed buildings.
Dogan posted her watercolour painting to social media and was subsequently arrested and sentenced.
Banksy’s mural, highlighting her first year in custody, has been painted on the historic Bowery Wall made famous by artist Keith Haring during the 80s.
The image was created with another artist, known as Borf, who has served time in prison for his graffiti.
Dogan has yet to hear about the mural, according to Banksy’s publicist.
The jailed artist is said to share a cell with 40 inmates, receiving only periodic visits.
An image of her painting was projected above the artwork on the evening of 15 March.