It happened just after 8 p.m. Sunday when police stopped at Bay Street and Portland Avenue.
There, they came in contact with two individuals outside a store. Police Chief James Sheppard says it's an area where police have encountered firearms and drug incidents.
Police say those two individuals fled before one of them was shot on Merrimac Steet.
"Officers were waived down by one of the store owners based on the fact that individuals were out in front of the store. The officers made the engagement and during the course of the pat frisk, they located the weapon. At that point in time, he broke from the one officer, there were two individuals they engaged, and both officers gave pursuit," Sheppard said.
During that pursuit, Sheppard says Tyshawn Johnson, 20, turned on police and displayed a gun. That's when Officer Cody Goodfriend fired once, hitting Johnson in the buttocks.
Goodfriend is currently reassigned to administrative duty.
Johnson was taken to Strong Memorial Hospital. He's been charged with criminal possession of a weapon. Sheppard says Johnson was armed with a sawed-off .410 guage shotgun.
"When we encounter someone who is armed, a lot of times we just have to deal with that circumstance. When our lives feel threatened, we're going to deal with that with deadly physical force," Sheppard said.
It was a busy Sunday for Rochester Police, as they responded to two other shooting incidents, including a triple shooting on Pierpont Street.
"I heard pop, pop, pop!"
Valerie Heard says those gunshots woke her and her family up around 2 a.m. Sunday.
When police arrived, they found an 18-year-old male shot multiple times. A 22-year-old man and 17-year-old girl were also wounded and went to the hospital in a private car. Police believe all three will be okay.
Neighbors say the shootings stemmed from a party on nearby Seyle Terrace.
"I don't let my teenagers go to house parties, that's the number one, I don't let them go. I usually let their friends come over here and I meet their parents and stuff like that," Heard said.
Then just after 12 a.m. Sunday, police responded to a call for someone shot at a house party on Brown Street. The victim, Florantina Nelson was shot in the upper torso. Police believe she was not the intended target.
Nelson, 26, was taken to Strong and has since been released.
The investigation into all three shooting incidents is ongoing. Anyone with information is asked to call 911.