Russell suffered damage to the cervical vertebra near the end of Saturday's win over Iowa State. He saw a specialist Monday and received the recommendation for surgery.
"Seth exemplifies the spirit and will of our football team," coach Art Briles said in a statement, "and through this our team will keep that spirit alive and well for him."
ESPN medical contributor Dr. Mark Adickes said about 30 percent of cases involving a broken facet joint bone in the neck result in surgery. Adickes said it is "unlikely" that the surgery will end Russell's career.
The typical recovery period for the surgery is six months, Baylor said.
Briles said Monday that he has confidence in true freshman backup Jarrett Stidham, citing his maturity, accuracy and polish.
"Seth has been masterful," Briles told ESPN's Joe Schad. "Jarrett is a guy who is as polished as anyone we have had a freshman. He is very, very accurate and has great instincts."
Stidham has played in every game this season and completed 85.7 percent of his pass attempts this season for 331 yards and six touchdowns. He was a five-star recruit who reneged on a commitment to Texas Tech.
He takes control of an offense that includes Corey Coleman, the FBS leader with a school-record 18 touchdown catches, and Big 12 rushing leader Shock Linwood. There is also a big, experienced offensive line led by All-American tackle Spencer Drango.
"Just makes all the difference in the world, especially with the offensive line that we have plus the dynamic skill people," Briles said. "It certainly takes a lot of pressure off that position, but you know the thing about it is, [Stidham] is a capable player. ... We're not putting a guy out there that's not capable. This guy's good. He's ready."
Stidham tweeted well wishes to Russell on Monday.
Prayers up to my man @S_Russell17. Great teammate and an awesome dude. Love you big dawg!— Jarrett Stidham (@Jarrett_Stidham) October 26, 2015
Sophomore Chris Johnson, who had been playing wide receiver this season, will be Stidham's backup.
The second-ranked Bears have an off week before traveling to Kansas State for a Thursday night game Nov. 5.
Russell had been one of the most productive quarterbacks in college football this year, remarkably accurate and a dangerous scrambler. He had thrown an FBS-leading 29 touchdowns this season and rushed for six touchdowns.
Information from The Associated Press contributed to this report.