The attack was carried out at the Ohio State University in Columbus by Abdul Razak Ali Artan.
Artan had spent seven years in Pakistan after leaving his native Somalia before coming to the US as a refugee two years ago.
The attack turns a spotlight on Republican President-elect Donald Trump’s calls during his campaign for a temporary halt to Muslim immigration while screening procedures are tightened.
Trump has since softened his stand, leaning towards heightened vigilance towards those coming from some countries linked to terrorism.
While national leaders were reluctant to even call the incident terrorism, a Republican Indian American Ohio lawmaker, Niraj Antani, jumped into the fray with a challenge.
Democrats see such acts as a result of the proliferation of weapons rather than the motivations.
In line with this Tim Kaine, who was the Democratic Party’s candidate for vice president, reacting to first reports of the shooting, tweeted that he was “deeply saddened by the senseless act of gun violence.”
State Representative Antani, who at 25 years is among the youngest elected officials in the US, tweeted back at Kaine, “But not saddened by the senseless act of machete or car violence?”
The tweet was later removed.
Columbus Police Chief Kim Jacobs told reporters that “we have to consider that it is” a terror attack.
Artan, whose age was reported to be between 18 and 20, was a third year transfer student in logistics management.
After leaving Somalia in 2007, he lived in Pakistan till 2014 before he came to the US. According media reports, Catholic Charities had helped with his family’s resettlement.
Officials said that after a university building was evacuated on Monday morning because of reports of a gas leak, Artan drove a car into the crowd of people standing outside, charged out of his car wielding a knife and attacked.
A police officer who was nearby reached the scene of the terror strike and shot Artan dead, officials said.
Officials did not release the names of the injured, who have all survived. One of them was a faculty member and most of the others were students, according to the Columbus Dispatch.
Al Qaeda and the Islamic State (IS) have called upon their supporters to carry out attacks by driving vehicles into people or using knives, tactics that do not require elaborate preparation or equipment or networks.
However, these can be potent weapons for sowing fear among the public.
The deadliest of the vehicle attacks by Islamic terrorists was in Nice in July when a man influenced by the IS drove a truck through a throng of people watching the French national day celebrations killing 86 people.
Trump had not, as of Monday night, said anything publicly about the Ohio attack showing uncharacteristic restraint after his strong statements on terrorism during the campaign.
Vice President-elect Mike Pence called it a “tragic incident” and expressed sympathy for the families of those affected.
In an interview with him published in the student newspaper, The Lantern, Artan had said, “I am a Muslim, it’s not what the media portrays me to be.”
He went on to blame the media for creating a picture of Muslims that would make people “feel uncomfortable” to see him praying in public.
But NBC news said that in a Facebook post attributed to him he wrote that he had reached a “boiling point” and added, “America! Stop interfering with other countries, especially Muslim Ummah [community]. We are not weak. We are not weak, remember that.