The U.S. Department of Agriculture rejected a waiver request by the state's Office of Temporary and Disability Assistance that would have allowed the city to implement the plan.
Mayor Michael Bloomberg says his administration is disappointed by the decision.
An official with the nation's food stamp program said in a letter Friday there were concerns about the plan's "potential viability and effectiveness."
The food stamp program was launched in the 1960s. It serves more than 40 million Americans each month.
The city's proposed ban would have been temporary so it could be evaluated.