The shooter was subsequently found dead of an apparent self-inflicted gunshot wound at the store in Collierville, an upmarket suburb of Memphis.

Collierville Police Chief Dale Lane said the shooting broke out at a Kroger store in his suburban community about 50km east of Memphis.

He said 13 people were shot, with 12 taken to hospital, some with very serious injuries.

One Kroger worker, Brignetta Dickerson, told WREG-TV she was working at a cash register when she heard what at first she thought were balloons popping.

"And here he comes right behind us and started shooting," Dickerson said.

"He kept on shooting, shooting, shooting. He shot one of my co-workers in the head and shot one of my customers in the stomach."

A police SWAT team and other officers went aisle to aisle in the store to find people who had sought cover or were in hiding, removing them to safety.

"We found people hiding in freezers, in locked offices. They were doing what they had been trained to do: run, hide, fight," the chief said.

"I've been involved in this for 34 years and I've never seen anything like it.

"It's going to take a little bit before we know what happened."

The identities of the shooter and the victims were not immediately released.

"We're going to carry this thing as far as we can to see and make sure that there's no else involved," Lane said, adding that there was "no credible evidence" there was a second shooter.

Collierville is a growing suburb of more than 51,000 people. Set in a rural and historic area, the town square has largely become known for its boutiques and bed and breakfasts.

Earlier this year, Tennessee became the latest US state to allow most adults 21 and older to carry handguns without first clearing a state-level background check and training.

The measure was signed into law by Republican Governor Bill Lee over objections from law enforcement groups and gun control advocates concerned the measure would possibly lead to more gun violence.

Australian Associated Press