Wilson will have a fusion of the vertebrae on Jan. 16, according to Ralph Vacchiano of the New York Daily News.
Wilson, the Giants' top pick in the 2012 draft, suffered a herniated disc in his neck on Oct. 6 and did not play again the remainder of the season. Doctors have told him the injury carries an increased risk of further damage if he continues playing, according to Pro Football Talk. He said during the season he plans to continue playing, but faces an uphill battle in rehabbing from surgery.
Giants owner John Mara addressed Wilson's injury in a radio interview on Thursday, telling WFAN he was unsure whether would be Wilson back for 2014.
"We're hopeful that David will be able to play for us again next year. Time will tell on that one."
But when asked whether he could count on Wilson being the No. 1 back, Mara said, "I don't think so."
With Wilson's future looking cloudy at best, the Giants will need to address the running back position this offseason. Andre Brown and Michael Cox, the team's remaining backs, combined for just 535 yards and a 3.3 yard average in 2013.
The 2014 runnning back free agent class is notably weak, with Houston's Ben Tate and an aging Maurice Jones-Drew topping the list. Chris Johnson could be another option if the Titans decide to rid themselves of his massive contract.
The draft class is not particularly strong either, with few backs getting first-round consideration. Top prospects include Arizona's Ka'Deem Carey, Auburn's Tre Mason, Washington's Bishop Sankey and Baylor's Lache Seastrunk.