Stillwater police Capt. Kyle Gibbs said the woman's sedan plowed into an unoccupied motorcycle of an officer who was working security at the parade, then into the crowd.
The driver of the sedan was taken into custody on a DUI charge, Gibbs said.
Gibbs said three people were killed and 22 were injured in the crash today morning.
Dave Kapple of Houston told the Stillwater News Press that he and his son were about 10 feet away when they saw the vehicle barreling into the crowd.
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Konda Walker, from Anchorage, Alaska, was attending the festivities ahead of the homecoming game between Oklahoma State and Kansas.
"At first we thought it was part of the show," Walker told the News Press.
"People were flying 30 feet into the air like rag dolls."
Phone calls to Oklahoma State officials were not immediately returned.
The university posted on Twitter: "Oklahoma State University is saddened by the tragic parade incident earlier this morning.
Our thoughts & prayers are with those affected.