On Monday, Woods' wife gave birth to the couple's first child.
Woods said May 21 he intended to play at Warwick Hills in Grand Blanc but the birth of his child was a priority.
The Buick Open is earlier this year than in the past, starting next Thursday and ending July 1 instead of in early August.
Woods has played at the tournament about 60 miles north of Detroit the past five years -- winning it in 2006 and 2002 -- and eight times in his career.
He has had a sponsorship agreement with Buick since 1999 and agreed to a new deal in 2004 believed to be worth more than $40 million over five years. Buick has said the contract does not require Woods to play in specific PGA TOUR events it sponsors.
He is scheduled to host a tournament in Washington, D.C., from July 5-8.
The British Open starts July 19, and the PGA Championship begins Aug. 9 at Southern Hills Country Club in Tulsa, Okla.