The woman who died was 26 years old and was identified by Atlanta news station 11 Alive as Brittany Macon.
Macon and the other woman shot were both relatively new employees, their boss said.
The other woman, 24, remained in critical condition Monday, Hampton said. The injured woman's 5-year-old son was in the restaurant at the time, and Hampton lamented the trauma that that child will have to deal with.
"It's frustrating that we have a 26-year-old female who is no longer with us," Hampton said. "It frustrates me that we had an individual with a firearm who decided that was the answer to resolve a conflict over a sandwich."
"It just breaks my heart to know that someone has the audacity to point a weapon and shoot someone for as little as too much mayonnaise on a sandwich," restaurant co-owner Willie Glenn told WSB-TV.