The New-York artist had requested to use the roof, which has sweeping views of Melbourne, for his next photographic installation Return of the Nude as part of the Chapel Street Precinct's Provocare arts festival.
But Woolworths denied the request in late April, saying it put local customers first and the request to use the space on a weekend would disrupt access to the store.
"At Woolworths, we will always put the convenience of our local customers first. We recently upgraded the rooftop car park at our Prahran store to make it more accessible and comfortable and its primary purpose is so our customers have convenient access to available car parking close to our store," a spokeswoman said.
"The request for the photo was for the weekend, which is the busiest time of the week for shopping in our stores, and as such we must ensure customers have convenient access to our store when we are open."
The spokesperson the company was a proud supporter of the Prahran community and remains supportive of the Provocare Festival of the Arts event.
Tunick and the Chapel Street Precinct Association have begun a petition top change woolworth’s decision.