The injury could be career-ending, the source said.
Wilson had spinal fusion surgery in January to repair a disk problem and wasn't cleared for contact until July 21. He practiced with the Giants for the first week of training camp, but he left the field Tuesday after a collision in practice with guard Eric Herman, and he was diagnosed with a burner.
The Giants sent Wilson to the Hospital for Special Surgery in New York for tests Tuesday night. Wednesday, they announced that he would sit out the remainder of last week's practices and Sunday night's preseason game.
He was scheduled to be examined Monday by Dr. Frank Cammisa, who is that hospital's chief of spinal services and who performed the fusion surgery on Wilson in January.
The Giants have said they would be thrilled if Wilson returned, but they also said all offseason that they'd be prepared in case he couldn't play again.
Williams had seven carries for 48 yards and scored on a 3-yard run in the Giants' 17-13 victory over the Buffalo Bills on Sunday night in the preseason-opening Hall of Fame Game.
ESPN.com Giants reporter Dan Graziano contributed to this report.