The new speedy delivery option was available to people in some parts of Manhattan who subscribe to Amazon Prime service, which has an annual membership fee of $99.
Prime Now delivery offers tens of thousands of common items such as batteries, towels and shampoo that could be ordered using Amazon applications on mobile devices powered by Apple or Android software.
"There are times when you can't make it to the store and other times when you simply don't want to go," Amazon senior vice president of worldwide operations Dave Clark said in a release.
"There are so many reasons to skip the trip and now Prime members in Manhattan can get the items they need delivered in an hour or less."
One-hour delivery comes with a charge of $7.99, while two-hour delivery is free with purchases, according to Amazon.
Prime Now will be expanded in New York and rolled out in more cities next year, Clark said.
Quickly sating desires of online shoppers has become a point of competition, with Google and a growing array of major retailers offering fast delivery. Car-sharing startup Uber is reportedly toying with the idea of drivers efficiently shuttling purchases to people.
Amazon has been investing heavily in its distribution network and is even experimenting with using aerial drones to make deliveries.
Prime Now is available in New York from 6:00 am to midnight daily, with Amazon's facility on 34th Street in Manhattan serving as a hub for deliveries.
Amazon Prime membership in the United States comes with free two-day shipping as well as access to streaming films, television shows and music.