Campbell last competed at the Charles Schwab Challenge, which concluded June 14.
"While the positive test result is unnerving, I am incredibly grateful to be asymptomatic and feel physically well, and my thoughts are with anyone dealing with (COVID-19), directly or indirectly," Campbell said.
"I support the Tour's protocol during this time and will be quarantining myself to protect others until I am well. I am looking forward to competing once again once it is deemed safe for me to make my return."
Harris English on Monday became the fifth PGA Tour player to test positive for COVID-19. He has also withdrawn from the tournament, which begins Thursday in Detroit.