The November 27 attack at OSU was carried out by one of its students, Somali-born Abdul Razak Ali Artan, the authorities said.
The ISIS-affiliated Amaq news agency called the 18-year-old business undergraduate a “soldier”.
Abdul Razak Ali Artan drove his car at a group of people, then attacked them with a knife before being shot dead.
Amaq posted an image of Abdul Razak Ali Artan wearing a blue shirt and sitting with greenery in the background, but did not say if the attack was directed from abroad, or if Artan had been self-radicalized.
Most of the victims were injured by the attacke’s car, but two were stabbed with a “butcher’s knife” and another suffered a fractured skull, officials said.
One of the wounded victims, William Clark, an OSU professor, described how Abdul Razak Ali Artan’s vehicle had crashed into a large concrete planter before bouncing off and striking him.
“It clipped the back of my right leg and basically flipped me up in the air and I landed on the concrete,” he told a news conference.
William Clark said Abdul Razak Ali Artan then got out of the car and began attacking students before he was shot down.
Surveillance photos showed the attacker in the car by himself just before the attack, but investigators are looking into whether anyone else was involved.
Dozens of FBI agents have searched Abdul Razak Ali Artan’s apartment for clues as to what may have triggered the attacks.
Neighbors described him as polite and said he attended daily prayers at a local mosque.
Abdul Razak Ali Artan, who was born in Somalia and was a US permanent resident, arrived in the country in 2014 as the child of a refugee.
He had been living in Pakistan from 2007 to 2014.
Abdul Razak Ali Artan recently posted on Facebook about the US treatment of Muslims, according to the AP, citing a law enforcement official who spoke on the condition of anonymity.
“If you want us Muslims to stop carrying lone wolf attacks, then make peace” with the Islamic State group, he allegedly wrote.
Representative Adam Schiff of California, the top Democrat on the House Intelligence Committee, said the act was indicative of someone who may have been self-radicalized.
ISIS militants have found recruits in the US Somali community in recent years.
About a dozen young men and women from Minnesota’s Somali community have traveled to Syria to join militant groups.
Nine men in Minnesota were sentenced on terror charges for plotting to join ISIS.
And a Somali-American man attacked 10 people with a knife at a central Minnesota mall before he was killed by an off-duty police officer in September.
Jaylani Hussein, the executive director of Council of American-Islamic Relations’ Minnesota chapter, said some Somali-Americans were concerned about being viewed as “guilty by association”.
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