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 surgery recommendation.
"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 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.
The new Baylor starter tweeted well wishes to Russell on Monday.
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.