They say the man caught on camera walked into the Subway restaurant on East 233rd Street in the Wakefield section on Saturday.
He allegedly showed the 15-year-old cashier a gun and demanded cash.
The suspect is described as standing about 5-foot-10 with band-aid under his left eye.
He was wearing a red sweatshirt and a Yankees cap.
Anyone with information in regards to this incident is asked to call the NYPD's Crime Stoppers Hotline at 800-577-TIPS.