The attacker, who was dressed in a security uniform and reportedly made references to Allah, was shot dead by an off-duty police officer on Saturday.
The so-called Islamic State claimed the man was one of its supporters, but the FBI said no link had been found.
The attack happened in St Cloud, 70 miles (110km) out of Minneapolis.
None of the victims suffered life threatening injuries.
The FBI's Rick Thornton said it was too early to say whether the attack was linked to international terrorism.
He said: "We are currently investigating this as a potential act of terrorism. And I do say potential. We do not at this point in time know whether the subject was in contact with, had connections with, was inspired by, a foreign terrorist organisation."
The attacker asked at least one person if they were Muslim, according to St Cloud Police Chief Blair Anderson.
An off-duty police officer shot and killed the suspect, Mr Anderson said.
The suspect, who has not been officially identified, was said to have been wearing the uniform of a private security firm when the attack occurred.
The media arm of IS said in a statement that the attacker had carried out the operation "in response to calls to target the citizens of countries belonging to the crusader coalition".
The FBI has said it is treating a stabbing attack at a shopping centre in Minnesota that injured eight people as a potential act of terrorism.