A shooting at a mall in New York caused a panic Saturday ... with people rushing to take cover in the back of a hair salon, in a bathroom and more -- and it was all caught on video.

Patrons of the Sangertown Mall in New Hartford, New York were going about their day ... when what sounded like gunshots rang out -- and people dove for cover.

Watch the clip ... while at first a group of people in a salon aren't sure what they heard after multiple shots are fired, they quickly jump into action, crowding in the back of the store for cover.

There's a lot of shouting as people try to herd one another to safety ... including one woman who is screaming for her daughter. Thankfully, the two are reunited before hiding together.

Tons of people sprint out of the store -- and, you can see the hallway full of people making their way to the exit ... though one family enters the salon and barricades themselves in the bathroom.

The panic slowly subsides ... and local reports say only one person was shot. Police have said this wasn't an active shooter situation -- which could indicate the shooting victim and the shooter actually knew each other.