Watney, who played in the first day of the South Carolina tourney on Thursday, woke up feeling ill Friday ... and, according to PGA Tour reps, tested positive shortly after.

FYI, the Tour tested EVERYBODY prior to the start of the week's tournament ... with all results -- including Watney's -- coming back negative.

The Tour says Watney will now have to undergo strict quarantine and isolation rules to eventually return to action ... and says it's taking precautions for everyone and everything that might have come in contact with Nick at this week's event.

"Nick will have the PGA TOUR’s full support throughout his self-isolation and recovery period under CDC guidelines," Tour officials said in a statement.

Watney played with Vaughn Taylor and Luke List in Thursday's opening round ... but neither golfer has withdrawn -- with both dudes still currently in the middle of their Friday rounds.