It’s believed the gunman was a Walmart employee.
Randall County Sheriff’s Office said: “The suspect has been shot by APD SWAT and has died. Hostages inside are safe.”
Earlier the Sheriff’s Office confirmed at least one hostage was being held.
The statement added: “We do consider this a work-place violence situation at this point.
“All agencies are on scene, including Amarillo SWAT, APD, RCSO, PCSO and DPS. The SWAT robot is currently being utilised.
“Although there were reports of shots fired when officers arrived on scene, there have been no confirmed injuries.”
Police and SWAT officers stormed the supermarket shortly before 6pm GMT.