Abdul Razak Ali Artan was shot and killed within minutes after plowing into the group by a police officer with less than two years on the force, said Monica Moll, director of public safety for Ohio State University.
"It frankly took a piece out of everybody here at our beautiful Ohio State University that this could have happened here," Ohio Governor John Kasich said at a news conference.
A U.S. government official confirmed the assailant was from Somalia, 18 years old and a lawful permanent resident of the United States. A second government source said investigators had reason to believe the attacker at the campus in Columbus was a Somali refugee. Columbus, the state capital, has a large Somali population.
U.S. Congressman Adam Schiff, a California Democrat and the ranking member of the House Permanent Select Committee on Intelligence, said intelligence agencies were assisting in the investigation.
"It bears the all of the hallmarks of a terror attack carried out by someone who may have been self-radicalized," Schiff said in a statement.
Another U.S. official told Reuters U.S. agencies are investigating the Columbus attacker’s background and motivations, but cannot clearly say yet whether he had any ties to suspected militant cells or groups.
The attack at the Columbus campus, which was initially reported by the university on Twitter as involving an "active shooter," drew a massive response of heavily armed police.
The suspect jumped the curb and used the vehicle to strike pedestrians in front of Watts Hall, Moll said.
The suspect left the vehicle armed with the knife and stabbed several others, Ohio State University Police Chief Craig Stone said.
"This was done on purpose,” Stone said.
Less than 2 minutes elapsed between the first call for help at 9:52 a.m. local time and the shots fired by campus police officer Alan Horujko, 28, Moll said.
The incident follows a stabbing attack in September at the Crossroads Mall in St. Cloud, Minnesota, where a man whose family came to the United States from Somalia wounded 10 people with a knife before he was shot to death by an off-duty police officer.
Authorities last month indicated the Minnesota attacker showed signs of radicalization and a Federal Bureau of Investigation special agent said his actions appeared to be "consistent with the philosophies of violent radical Islamic groups."
One person was critically injured in Monday's incident, Columbus fire officials said. Eleven people were treated at area hospitals, including 10 taken by ambulance.
Ohio State University Wexner Medical Center treated six victims, said Dr. Andrew Thomas, the chief medical officer. They included two with stab wounds and three others who had injuries from being hit with the vehicle.
Two other hospitals received five patients, who suffered from lacerations and injuries caused by the vehicle, Thomas said.
With nearly 60,000 students, the Columbus campus is the state's flagship public university.
CNN aired an image from a room at the university where students had barricaded a door with stacked chairs.
Columbus and university police continued their investigation with assistance from the FBI. The attack prompted university officials to warn students on Twitter to shelter in place.
Ohio State lifted the order shortly before noon EST.
The university campus remained open, although classes were canceled for the day.
President Barack Obama was briefed on the incident by Lisa Monaco, his homeland security adviser, said White House spokesman Josh Earnest.