The single-engine plane went down in the Winona Wildlife Management Area near Perryville, located about 45 miles west of Little Rock.
Officials said Budke and assistant coach Miranda Serna were on a recruiting trip. Oklahoma State's president is now calling on the campus to pull together as a family.
"This is our worst nightmare. The entire OSU family is very close, very close indeed," OSU President Burns Hargis said at a news conference. "To lose anyone, especially these two individuals who are incredible life forces in our family, it is worse beyond words."
Two others on the plane, 82-year-old former Oklahoma state Sen. Olin Branstetter, who was flying the plane, and his wife Paula, also died in the crash.
The cause of the crash is under investigation.
The Associated Press contributed to this report.