Walker was taken by ambulance to a Tulsa hospital after colliding helmet-to-helmet with a teammate in the first half of a 45-10 loss to the Golden Hurricane.
Walker had stopped breathing but was revived by emergency personnel using CPR, Fox Sports reported.
Tulane team physician Dr. Buddy Savoie said after the game the player had sustained "a cervical spine fracture" and surgery was expected Sunday or Monday, The Tulsa World reported.
"He was stable when we transported him (to St. Francis Hospital)," Savoie told the newspaper. "I do not think -- based on the information that we have -- that his life was ever in danger or was ever at risk."
"Mood in the locker room was somber," Tulane head Coach Curtis Johnson wrote on the school's Twitter feed. "Definitely one of the most difficult times."
The school indicated Walker was still in stable condition at the hospital.