It is alleged a gunman with an assault rifle entered the store and opened fire at around 8pm on Sunday.
The apparent incident took place at a branch of supermarket giant Walmart in Hobart, a town on the outskirts of Chicago in the state of Indiana.
There are unconfirmed reports of multiple fatalities.
Local media are reporting that the FBI, as well as local and state police, are on the scene.
One local journalist said one or more suspects may have been detained.
Witnesses reported seeing blood on the floor.
One said: “I was laying on the ground and I could hear the victim who had been shot.”
The Mayor of Hobart, Brian Snedecor, posted a statement on Facebook.
He wrote: “There are many false and inaccurate comments being made on Facebook in regards to the incident at the Hobart Walmart.
“The Police are on the scene and conducting an investigation.
“A statement at the appropriate time will be provided by the Chief”.
Hobart Fire Department tweeted: “Waiting for official word from the Hobart Police concerning the incident at Walmart tonight.
“Please be patient.”
A Twitter user added: “My work is like two minutes away from the Hobart Walmart.
“We were not surprised at all when we were told there was a shooting.”
Hobart has a population of approximately 30,000.
More to follow…