Crushing the plans, the authority also said Amazon's drones, which are designed to travel at up to 50 miles an hour and carry packages of up to 20kg, could not be flown out of sight of the pilot.
Using drones for commercial use is already banned in the US, but last year Amazon wrote to the FAA asking for permission to test the drones on its own premises away from aviation hubs and urban areas.
It is understood the company will continue testing drones in other markets where they are not banned, for example in India. Amazon claims its drones system is capable of launching as soon as regulation allows.
Paul Misener, Amazon's vice-president of global public policy, said in a statement to Digital Spy: "We are committed to realising our vision and are prepared to deploy where we have the regulatory support we need."
Amazon is not the only company to experiment with drones, DHL, Coca-Cola and Google X all have similar programmes. However, a retail futurologist told Marketing last month it would be unlikely drones would soon become the future of deliveries, brushing it off as a PR exercise designed to show off capability.