39-year-old Watney dropped out of the RBC Heritage Tournament at Hilton Head, South Carolina on Friday before the second round.
He flew privately for the tournament, which began Thursday and was not on a charter plane offered by the PGA Tour, the company said.
“Nick is fully supported by the PGA Tour during his self-isolation and recovery period as per CDC guidelines,” the PGA Tour said in a statement.
“For the health and well-being of all those involved with the tournament, the Tour began implementing its response plan, including consultation with medical professionals and working closely with Nick.”
Watney, a five-time winner of the PGA Tour, played with fellow Americans Vaughn Taylor and Luke List in the first round and carded a three-over par 74.
A total of 369 people, including players, caddies and required personnel, were tested for Kovid-19 before the tournament began, the PGA Tour said. All those tests were negative.
The PGA Tour declined to comment further and urged news organizations and fans to respect Watney’s privacy.
The Heritage Tournament is the second since the PGA Tour has resumed following a suspension due to a coronavirus pandemic. It is played without audiences and with strict protocols.
American Daniel Berger won the Charles Schwab Challenge in Texas last week, and the world’s top golfers returned to the competition after a three-month hiatus.
CNN’s Jill Martin contributed to this report.