Gary police said they responded to the grocery store in the 2100-block of Malcolm X Drive at about 7:29 p.m. Monday and found a man dead inside.
After speaking with witnesses and reviewing video, police said two men got into a fight at a checkout counter. Police said one man took out a gun and shot the victim.
The shooter then picked up his items and walked out of the store, leaving his debit card at the cash register, police said.
Police then arrested the suspect, a 44-year-old Gary man, walking in the area of the 600-block of East 20th Avenue.
Police said the victim is a 48-year-old man from Gary. Authorities have not released his identity.