The victim is identified as 25-year-old Randall Grimm.
Police say under arrest and booked for the killing is 40-year-old Sidney S. Andersen.
Police say at 8:46 p.m. Monday evening officers were sent to the grocery store for a report of a man with a gun. Then the call was changed to a "shots fired" call.
When officers arrived they found Grimm down outside on the east side of the store. He appeared to have been shot. Grimm was pronounced dead at the scene.
Officers located a possible suspect, Sidney Andersen, inside the store and he was transported to Central Police Headquarters for questioning.
No employees or customers of the store were injured.
For the people inside the store at the time, it was somewhat confusing. One witness tells Channel 6 News that just before 9 p.m. Monday, he saw several officers with their guns drawn inside the store. He says they had somebody in handcuffs after what he thought was an attempted robbery.
Rob Charlson says he was in the deli, about 10-feet away, when he saw, "Two officers pointing their gun at a gentleman, telling him to get on the ground." Charlson saw him comply. Once on the ground, officers cuffed the suspect.
A store employee said there was no robbery attempt. He says a man shot the victim outside of the store and then ran inside, where he was apprehended by a security guard and then police.
One woman who was just about to go shopping at the store says she heard three shots fired. "I was coming to buy groceries," Mary Ekstrom told Channel 6 News, "And as I was headed for the front door, I heard three gun shots."
She adds, "I feel badly, because I heard the victim died... it's troubling people resort to guns."