Wilson is expected to be sidelined at least a few weeks. The timetable for his return might change after Watkins examines him and makes a determination.
The running back has already been ruled out for Thursday night's game against the Chicago Bears. On Tuesday, Giants coach Tom Coughlin called Wilson "week to week."
Wilson tweeted on Thursday that he wished he was able to play against the Bears.
Wishing I could play wit my team today but wishing them the best and I know they gonna bring this win home #Goodluck
— David E. Wilson (@4stillRunning) October 10, 2013
Wilson left Sunday's game against the Philadelphia Eagles after the final play of the first quarter when he felt tingling in his arms. He was examined and treated for a neck injury, according to the team.
To replace Wilson on Thursday night, the Giants re-signed running back Da'Rel Scott, who had been cut last week. Scott and Brandon Jacobs are likely to split the carries in Wilson's absence against the Bears, though there remains a chance rookie Michael Cox could work his way into the mix as well.
If Wilson must miss more than one game, the Giants could find themselves in the market for a veteran free agent. There are 10 days between this game and their next one.
One of the reasons the Giants brought back Scott was that they had only three days to prepare for the game against Chicago and he already knew the playbook.
ESPN NFL Insider Adam Schefter and ESPN.com Giants reporter Dan Graziano contributed to this report.