Watney, 39, withdrew from the RBC Heritage tournament at Hilton Head, South Carolina, Friday before the second round.
He privately traveled to the tournament that began on Thursday and was not on the charter flight offered by the PGA Tour, the organization said.
“Nick will have the full support of the PGA Tour throughout the period of self-isolation and recovery according to CDC guidelines,” the PGA Tour said in a statement.
“For the health and well-being of everyone involved in the tournament and those in the community, TOUR began implementing its response plan in consultation with medical professionals, including working with those who may have had close contact with Nick.”
Watney, a five-time PGA Tour winner, played in the first round with Americans Vaughn Taylor and Luke List, drawing with 74 over a triple, which is out of rhythm.
A total of 369 individuals, including players, caddies and core staff, were tested on Covid-19 before the start of the tournament, the PGA Tour said. All of these tests were negative.
The PGA Tour declined further comment and demanded that news organizations and fans respect Watney’s privacy.
The Heritage Tournament is the second to be held since the restart of the PGA Tour following the suspension due to the coronavirus pandemic. The game is played without spectators and with strict protocols.
American Daniel Berger won the Charles Schwab Challenge in Texas last week, while the world’s best golfers returned to action after a three-month hiatus.
CNN’s Jill Martin contributed to this report.