Investigators say that they believe Woods mistakenly hit the accelerator rather than the brake as he was negotiating a curve in February in the Los Angeles area.
"This is purely an accident," the Los Angeles County sheriff said, adding there's no evidence Woods was intoxicated. The golfer is awake and responsive after a "long surgical procedure."
The legendary golfer suffered "multiple leg injuries," according to his agent. The sheriff's department said Woods was driving the only car involved in the collision.
Trump has long been a fan and recently, a business partner of Woods. He announced his decision to give the award to Woods in a tweet after Woods won the Masters tournament last month at age 43.
Woods' historic victory Sunday at the golf Masters Tournament shows the continued earning power of a player who was dropped by many of his sponsors over the course of a tumultuous decade.
The all-time golf great was booked Monday morning in Jupiter, Fla., on suspicion of driving under the influence. He was released just a few hours later.
Also this week: The story of a 60-year-old United Airlines pilot and runner who finished the New York City Marathon in 2 hours, 47 minutes and 27 seconds.
Woods, who hasn't won a golf tournament in two years, entered the Wyndham Championship Sunday trailing by just two shots. The stage was set for something remarkable, but the magic didn't happen.