The blind Grammy Award-winning artist had surgery Thursday at Wake Forest Baptist Medical Center after a fall Monday at his home, CNN reported.
Mitch Greenhill, the singer's representative, initially said Friday that Watson was "resting and responsive."
"He has regained some strength," Greenhill said on Watson's Web site. "The family appreciates everyone's prayers and good wishes."
A follow-up procedure Saturday, though, left him in critical condition, CNN said.
The influential folk musician, best known for his flatpicking and fingerstyle technique on the guitar, has won seven Grammy awards and a Grammy Lifetime Achievement Award.
Watson said his father gave him the push to learn to play guitar.
"One day he brought (a banjo) to me and put it in my hand and said, 'Son, I want you to learn how to play this thing real well,' " Watson told National Public Radio's Terry Gross in 1988. "It might help you get through the world."