The 15-time major winner underwent surgery for significant leg injuries after his car left the road and tumbled down an embankment near his home in California.
He is currently recovering at Harbor-UCLA Medical Centre.
"We thank everyone for the overwhelming support and messages during this tough time," a statement on his official Twitter account said.
"As previously communicated Tiger was involved in a single-car accident early this morning in California. He has undergone a long surgical procedure on his lower right leg and ankle after being brought to the hospital.
"He is currently awake, responsive, and recovering in his hospital room."
An update from the hospital following his admission and treatment said: "Mr Woods suffered significant orthopaedic injuries to his right lower extremity that were treated during emergency surgery by orthopaedic trauma specialists at Harbor-UCLA Medical Center, a level 1 trauma centre.
"Comminuted open fractures affecting the upper and lower of the tibia and fibula bones were stabilised by inserting a rod into the tibia. Additional injuries to the bones of the foot and ankle were stabilised with a combination of screws and pins.
"Trauma to the muscle and soft tissue of the leg required surgical release of the covering of the muscles to relieve pressure due to swelling."
After undergoing surgery on a back problem earlier this year, Woods had hoped to return to competitive action at the Masters in April. That now seems unlikely, but is yet to be officially ruled out.
"Tiger Woods is part of the Augusta National family, and the news of his accident is upsetting to all of us," Masters chairman Fred Ridley said via social media.
"We pray for him, for his full recovery and for his family during this difficult time."
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