The organisation added it stands in full support of Woods and has "sincere hope for his strength, comfort, and recovery", and will share further updates on the future captaincy "when appropriate".
Woods has competed at the Ryder Cup eight times for the USA, with his first appearance in 1997 and last in 2018. However, he has only won the biennial showpiece once in 1999 - at Brookline in Massachusetts.
The 2027 Ryder Cup between the US and Europe will take place at Adare Manor in County Limerick, Ireland, from 17-19 September.
Keegan Bradley captained the US team at Bethpage Black last year and Woods was among the favourites to take the role next year.
When asked about the captaincy in recent months, Woods has said he was undecided.
Luke Donald's third term as European captain for 2027 was confirmed last month.

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