A man entered the supermarket and fired a rifle, a law enforcement official told ABC News.
They added that the scene is no longer active and there are no other suspects outstanding.
New York Governor Kathy Hochul has stated that assistance is offered to local officials.
She wrote on Twitter: “I am closely monitoring the shooting at a grocery store in Buffalo. We have offered assistance to local officials.
“If you are in Buffalo, please avoid the area and follow guidance from law enforcement and local officials.”