Law enforcement shot and killed one suspect, according to local television station WBNS, which reported that police led two people out in handcuffs from a garage they had surrounded on the university's main campus in Columbus.
A witness suggested that a suspect was driving a red SUV.
The incident was called an active shooter situation, but it was unclear whether any of the victims had suffered firearm injuries.
Some reports suggested the attacker or attackers used a knife.
Television footage showed students leaving school buildings as Rebecca Diehm, spokeswoman for the Columbus fire department, said eight people had been transported to hospital.
One was in critical condition, and the rest were stable, she said.
OSU Wexner Medical Center tweeted that it was treating four victims, none with life-threatening injuries.
Earlier the university's emergency management service had urged students and staff to shelter in place amid reports of an active shooter, as SWAT teams fanned out across the facility.
Details were murky as the situation unfolded. One student told MSNBC she was walking along a road on campus when a car plowed into a group of people, including a police officer.
Another student, Joseph Noll, said he heard a fire alarm, but no shooting -- and also said a car had driven into the crowd.
"I was right there, and there was no one shot," he told WBNS. "Someone DID run over a crowd of people with their car. I can tell you that for sure."
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