Police said the shooting happened at about 9:12 a.m. at the Evergreen Park Mariano's on 95th Street.
Dorian Johnson had just pulled into the parking lot when he saw customers running out of the store.
"I was sitting, I'm about to go in and next thing you know, everybody is just in the parking lot frantic," Johnson said. "Only thing that stopped me was I was on the phone, so I was about to walk in. The lady right next to me, she had just walked went in, and it was bad."
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Police said video from inside the store shows the suspect following a 21-year-old woman into the store before he allegedly shot her in the back storage room.
"I've seen her plenty of times. I shop here real frequently, so it's kind of really sad," Johnson said.
Customers were inside when the gunfire rang out, but no one else was injured.
After the shooting, the suspect left in his vehicle. Within an hour, police were able to track down the man, who was still driving at the time. That suspect is now in custody.
Chopper 7HD was over the scene in the 1400 block of W. Thorndale Avenue as authorities arrested him in a red Ford Focus.
"This victim was a previous employee at the Amazon store in Oak Lawn, and had left there. Had an incident over there with this individual, the suspect, and left that store and began employment over here," said Evergreen Park Police Chief Michael Saunders. "Chicago police were, within an hour, through their camera system, able to make an arrest up north, with a suspect in his car, with a firearm, and he's in custody right now."
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Police tweeted out that they believe the shooting is related to a domestic situation, and there is no threat to the public.
The Mariano's and surrounding stores have been closed in the meantime while police investigate.