"We commend Tiger for prioritizing his long-term health and have great respect for the courage it takes to make such a personal decision," the PGA of America said in a statement.
Woods confirmed in February that the PGA of America had contacted him about captaining the US team in next year's Ryder Cup at Adare Manor in Ireland.
Woods has denied allegations that he was under the influence in connection with the accident. A breath test after the incident detected no alcohol, but Woods, 50, refused to submit to a urine test.
Europe has won the last two Ryder Cup tournaments. The United States has not lifted the trophy on European soil since 1993.
