The incident happened inside Plaza La Familia in Patchogue around 9 p.m. on October 23.
Authorities say the suspect approached a man inside the store, then assaulted him with his hands and feet before stabbing him with an unknown object.
The suspect is described as a heavy set Hispanic male with black hair that is short on both sides. He also has a tattoo of barbed wire on his right bicep and was last seen wearing a white T-shirt and a white baseball cap.
Suffolk County Crime Stoppers offers a cash reward of up to $5,000 for information that leads to an arrest.
Anyone with information about this crime is asked to call anonymously to Crime Stoppers at 1-800-220-TIPS.