The former world No.1's decision comes after he said he would step away from golf to focus on his health and wellbeing.
Woods was charged with driving under the influence after being involved in a car accident last week.
"We commend Tiger for prioritising his long-term health and deeply respect the courage it takes to make such a personal decision,'' the PGA of America said in a statement on Wednesday (Thursday AEDT).
"Tiger has shared with us that he will not serve as captain of the 2027 US Ryder Cup team and we support his decision."
A motion filed on Wednesday by his attorney, Douglas Duncan, asked that Woods be allowed to travel outside the country to begin "comprehensive inpatient treatment".
Duncan said the recommendation from Woods' doctor was based on the golfer's "complex clinical presentation and the urgent need for a level of care that cannot safely or effectively be done within the United States as his privacy has been repeatedly compromised".
Martin County Court Judge Darren Steele approved the motion, which did not say where the inpatient treatment facility was located.
Fifteen-time major winner Woods had been favourite to take on the US captaincy for next year's Ryder Cup in Ireland.
However, last Friday's events have changed the picture, with the 50-year-old escaping unhurt from an accident in which he clipped a trailer he was attempting to overtake and rolled his Land Rover.
Police reported that he showed signs of impairment, and investigators found two white pills identified as hydrocodone - a prescription opioid used to treat severe pain - during a search of his vehicle.
It was the fourth occasion he had been involved in a motoring accident since 2009.
"I know and understand the seriousness of the situation I find myself in today," Woods said in a statement on social media platform X. "I am stepping away for a period of time to seek treatment and focus on my health."
Woods was also charged with property damage and refusal to submit to a lawful test following last week's incident on Jupiter Island, Florida.
Before the incident there had been speculation over whether Woods might play at next week's Masters - an event he has won five times.
That will now not happen, and former European Ryder Cup captain Paul McGinley believes goodwill towards Woods is starting to fade.
"A lot of people are running out of patience now, including himself and his family by all accounts from what he said yesterday,'' said the Irishman, who oversaw Europe's 2014 Cup triumph.
"He realises the seriousness of the situation and I think it's a line in the sand."
- with AP
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