People in two vehicles got into an argument when one of them opened fire around 10:53 a.m. in the parking lot at 7001 Vollmer Road, Matteson spokesman Sean Howard said.
A vehicle was struck by the gunfire but no one was injured, officials said. The shooter and victim had left in their own vehicles, officials said.
At least six evidence markers could be seen scattered along one row of the parking lot.
Police have identified a person of interest, Howard said, but no arrests were announced.
The shooting was an isolated incident between the two people, Howard said. "This is not an active shooter incident," he said.
FOX 32 News has reached out to Amazon for a statement.
Matteson is roughly 30 miles south of Chicago.
The Sun-Times Media Wire contributed to this report.