Dr. Buddy Savoie said during a postgame news conference that Walker is in stable condition and will need spinal surgery in the "the next day or two."
"He was stable when we transported him," Savoie said. "I do not think, based on the information we have, his life was ever in danger."
Tulsa was leading 35-3 and facing a fourth-and-2 with the ball at the 33-yard line when the Golden Hurricane called timeout. Tulane then called timeout.
When play resumed, Tulsa quarterback Cody Green tossed a short pass to Willie Carter, who caught it at about the 28, and turned upfield. He was tackled around the 18-yard line, with defensive tackle Julius Warmsley and Walker sandwiching him and apparently smashing the crowns of their helmets into each other.
Medical personnel from both teams came out about 12:37 p.m. to attend to Walker as he lay on the field.
Savoie said after the game that Walker "actually never completely lost consciousness" and was breathing.
About 12:52 p.m., he was lifted onto a stretcher and loaded into a waiting ambulance about two minutes later. The ambulance drove off the field about 1 p.m.
FOX Sports reported a hush went over the crowd at H.A. Chapman Stadium as Walker was attended to on the field, and that several coaches were in tears. Spectators bowed their heads as someone on the field led the stadium in prayer.
The game resumed at 1:20 p.m.
Later Saturday, Tulane Athletics said in a statement that Walker had been placed in traction and was undergoing treatment for a "lot of swelling in his neck."
"The current plan is for him to have surgery in the next one to two days. He is being treated by specialists," said the statement posted on Tulane University's website. It added that the physicians in Tulsa were doing a "great job" taking care of Walker.
Walker is a senior majoring in cell and molecular biology. His brother, Raynard, told The Associated Press that their mother was watching the game on television when her son was injured.
Tulane head coach Curtis Johnson said after the 45-10 loss that while Walker was on the field, Johnson told Walker that he was praying for him and that help was on the way.
He said the mood among players was somber, and called the day his most difficult ever.
"Just seeing a young man, one of our family members, on the ground. It was just difficult for our guys," Johnson said in the postgame conference. "It's no excuse, but I don't know if they could have focused.
"It was tremendous that they finished the game, as I thought about just saying `Hey look, let's not do anything else. Let's just get on the road and go.' "