The attacker, who was was wearing a private security uniform when he struck in St Cloud, Minnesota, was shot dead by an off-duty officer, authorities said.
St. Cloud Police Chief Blair Anderson said the knifeman made references to Allah during his attack and asked at least one person if they were a muslim.
He told the St Cloud Times: “We will be diligent and get to the bottom of this.”
Mr Anderson added that no one else was thought to be involved in the violence at Crossroads Center mall and the FBI had offered to help investigate.