Three adults were pronounced dead at the scene, while the fourth victim, a two-year-old boy, died from his injuries at a hospital, according to a Stillwater police statement.
Nikita Nakal of Mumbai was identified as among the victims of the accident yesterday by University of Central Oklahoma (UCO) President Don Betz.
Authorities identified the driver as 25-year-old Adacia Avery Chambers, who was taken into custody on suspicion of driving while under the influence of alcohol.
She first hit a police officer's motorcycle and then rammed her car into the parade-goers packed on a street corner.
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Megan Lantz of Ponca City, Oklahoma, told the Oklahoman newspaper that about 100 people were standing on the corner at the time the car, going between 72-80 kph, struck the crowd.
Mayor Gina Noble and Stillwater City Council said, "we are heartbroken about the tragedy, and our hearts and prayers are with the families of those who died and are injured."
Some of the victims are children, authorities said.
In a statement posted on the University of Central Oklahoma website, Betz expressed condolences to the family of Nakal.
"While our thoughts and prayers are with the Oklahoma State University (OSU) community....Following the tragic events during OSU's homecoming parade this morning, it is with deep sadness that I ask you to extend those sentiments to the family and friends of one of our own students.
"Nikita Nakal of Mumbai, India, an MBA student at UCO, was among those who died," he said in the statement.
He said the university plans to honour Nakal soon.