Watney, 39, withdrew from the RBC Heritage tournament in Hilton Head, South Carolina, on Friday before the second round.
He traveled privately to the tournament, which began on Thursday, and was not on the charter flight offered by the PGA Tour, the organization said.
“Nick will have the PGA Tour’s full support throughout his self-isolation and recovery period under CDC guidelines,” the PGA Tour said in a statement.
“For the health and well-being of all associated with the tournament and those within the community, the TOUR has begun implementing its response plan in consultation with medical experts including working with those who may have had close contact with Nick.”
Watney, a five-time winner on the PGA Tour, played with fellow Americans Vaughn Taylor and Luke List in the first round, carding a three-over-par 74, well off the pace.
A total of 369 individuals, including players, caddies and essential personnel, were tested for Covid-19 before the tournament began, the PGA Tour said. All those tests were negative.
The PGA Tour declined to comment further, and asked that news organizations and fans respected Watney’s privacy.
The Heritage tournament is the second to be held since the resumption of the PGA Tour following its suspension due to the coronavirus pandemic. It is being played without spectators and with strict protocols in place.
American Daniel Berger won last week’s Charles Schwab Challenge in Texas as the world’s top golfers returned to competition after a three-month hiatus, with Watney also in action, missing the cut after finishing five-over-par for his two rounds.
CNN’s Jill Martin contributed to this report.