HBO scout Linda Perkins said the plan had been for 80 to 100 cast and crew to work on Shelter Island for roughly 72 hours, during which time they would use the local restaurants, bars and accommodation.
A resident told Page Six the locals were"annoyed" about the council's reaction, saying: "The councilors made this big deal about filming, when it would have given the locals a lot of money in food and money."
The news puts brakes on Nicole's latest venture, with no word on whether the team at HBO has found a suitable alternate location.
Earlier this month, Nicole opened about her painful divorce from Tom Cruise in 2001.
In an interview with Australian Women's Weekly, the Oscar-winner credited fellow Hollywood actor Hugh Jackman and his wife Deborra-Lee Furnish for helping her through the hardest times.
"They were some of my best friends during that period," she revealed.
Nicole has been happily married to Australian musician Keith Urban since 2006.
The couple are parents to daughters Sunday Rose, 10 and Faith Margaret, eight.