DeSoto County Sheriff Bill Rasco told the Commercial Appeal newspaper that the suspect had been shot and wounded in the incident in the city of Southaven.
The two people shot dead were believed to be Walmart employees, the sheriff said, and the suspect had been an employee until Monday.
A Walmart employee told a local television station that the gunman had worked at the store for 25 years before being fired.
A customer identified as Phil Cox, 70, said he was leaving the store for his car when he heard gunfire.
"I think the guy was going after employees," Cox told the Commercial Appeal.
The sheriff said the suspect and wounded police officer had been taken to local hospitals.
Southaven is a suburb of Memphis, Tennessee, which lies just to the north over the state line.