The two-time PGA Tour winner, who had been due to join compatriot Billy Horchel in flying the Stars and Stripes in the $5 million event, revealed the disappointing news in a post on Twitter.
He wrote: “Unfortunately, due to a persisting health issue, I’ve made the decision to withdraw from the @dunhilllinks this week so that I may fully recover. To avoid any potential for speculation, I don’t have Covid.”
Finau played in the tournament, which is held at St Andrews, Carnoustie and Kingsbarns, in 2019, finishing in a tie for tenth behind Frenchman Victor Perez.
“Withdrawing from a tournament is never something that I take lightly, and I wish all of the pros and amateurs an incredible week in Scotland,” added Finau.
“The Dunhill is an awesome event, one that I regret missing and one that I look forward to returning to in the future.”
Playing in his second Ryder Cup, Finau teamed up with Harrish English to beat Rory McIlroy and Shane Lowry 4&3 in the first-day fourballs at Whistling Straits.
European captain Padraig Harrington returns to play action in this week’s event along with three of his players at Whistling Straits, two-time Dunhill Links champion Tyrrell Hatton, Shane Lowry and Tommy Fleetwood.
Horschel is bidding to land this title to his success in the BMW PGA Championship at Wentworth earlier in the month.