There were conflicting reports about whether the gunman - armed with an AK-47 assault rifle - was among the dead or was in custody after the attack.
Police confirmed there were "multiple shootings" at the upmarket Ward Parkway complex in Kansas City, Missouri.
Joe Vitale, a fire department battalion chief who was at the scene, said: "We have at least two fatalities, maybe more."
According to local media reports, the suspect shot a police officer in the arm during a traffic check and then drove to the shopping centre where he opened fire.
Police were notified at around 4pm local time that a man was firing shots in the mall and that several people had been hit.
One eyewitness described how he heard three or four shots near the checkout aisles of a department store.
Aaron Washington, 34, who works at the mall, said he was coming back from lunch when he heard gunshots, and saw one man holding his eye.
"The man had apparently been shot," Mr Washington said.
Authorities evacuated a cinema in the complex and surrounding streets also closed.