Kyle Loven, a spokesman for the FBI regional office in Minnesota, said the agency was aware of the claim of responsibility and was working with local police.
The man, who was wearing a private security uniform, made references to Allah and asked at least one person if they were Muslim before he assaulted them at the Crossroads Center mall in St. Cloud on Saturday, the city's Police Chief William Blair Anderson told reporters.
"Whether that was a terrorist attack or not, I'm not willing to say that right now because we just don't know," Anderson said at a news conference.
In an interview with CNN on Sunday, Anderson said eight or nine people were wounded in the attack. Authorities had said earlier there were eight victims but one injured person transported himself to a hospital and was not initially counted, Anderson said.
Amaq, the news agency affiliated with the Middle Eastern extremist group Islamic State, issued a statement on Sunday saying, "The executor of the stabbing attacks in Minnesota yesterday was a soldier of the Islamic State and carried out the operation in response to calls to target the citizens of countries belonging to the crusader coalition."
Reuters was not immediately able to verify the Amaq claim.
Kyle Loven, a spokesman for the FBI regional office in Minnesota, said the agency was aware of the claim of responsibility and was working with local police in the investigation. A representative of the U.S. National Security Council also said it was aware of the claim but deferred to local investigators.
The knife attack in St. Cloud, a community about 60 miles (100 km) northwest of Minneapolis-St. Paul, came at a time of heightened concern in the United States about the threat of violence in public places.
An explosion rocked New York City's bustling Chelsea district on Saturday, injuring 29 people in what authorities described as a deliberate criminal act. But both New York Governor Andrew Cuomo and New York City Mayor Bill de Blasio said there was no indication it was linked to international terrorism.
In St. Cloud, the attacker entered the mall in the evening as it was busy with shoppers, Anderson said. He attacked his victims at several sites in the shopping center, which will remained closed on Sunday as police investigate, the police chief said.
Eight wounded individuals were transported to St. Cloud Hospital but none were believed to have life-threatening injuries, said Chris Nelson, a communications specialist for the medical facility.
One victim was expected to remain there, but the other seven patients had already been released or were expected to be let go shortly, officials said.
Anderson gave no details of the identities of the victims.
Police officials said they were still interviewing witnesses hours after the attack.
The off-duty police officer who shot the suspect was from a jurisdiction outside of St. Cloud, Anderson said. He would not say which agency employs the officer.