The suspect, whose name was not immediately released, was arrested and then taken to a hospital after complaining of chest pains, Memphis Police Sgt. Vince Higgins said. Higgins said authorities had not determined a motive for the attack.
The attack started in the manager's office of the Schnucks supermarket in Arlington, on the outskirts of Memphis, then spilled out into the store, Higgins said.
By the time the suspect was tackled, six women and two men were bleeding from stab wounds, he said. Police said two large kitchen knives used in the attack were found at the scene.
The ages of the victims were not immediately released. Higgins and a company spokeswoman said all the victims were employees of the store.
Four were in critical condition at area hospitals, Higgins said.
"Our first priority is the customers and associates," said Schnucks Markets Inc. spokeswoman Lori Willis said. She said officials from the St. Louis-based company were on their way to the scene.