The shooting happened outside of Sam's Convenience Mart on Academy Avenue in Middletown late Tuesday afternoon.
According to investigators, there was an altercation outside the store which continued inside. When police responded, they saw the suspect running out with a knife chasing another guy.
Two officers opened fire, officials said, but it is unknown how many times that they fired.
The man was taken to Orange and Rockland Medical Center where he was pronounced dead.
Authorities do not know the identity of the suspect. He was not carrying any identification, officials said.
New York State Police are investigating.