The former world number one blamed "an unexpected reaction to prescribed medications" following his arrest on Monday morning close to Jupiter Island, Florida, near his home.
He was released from Palm Beach County Jail at 10.30am, with a mugshot showing him looking tired and unshaven.
A statement from Woods read: "I understand the severity of what I did and take full responsibility for my actions.
"I want the public to know that alcohol was not involved. What happened was an unexpected reaction to prescribed medications. I didn't realise the mix of medications had affected me so strongly."
Despite the claim, the 41-year-old went on to apologise for the incident.
He added: "I would like to apologise with all my heart to my family, friends and the fans. I expect more from myself, too. I will do everything in my power to ensure this never happens again.
"I fully co-operated with law enforcement, and I would like to personally thank the representatives of the Jupiter Police Department and the Palm Beach County Sheriff's Office for their professionalism."
A spokesperson for the Jupiter Police Department had earlier confirmed to Press Association Sport: ''He (Woods) was arrested for suspicion of DUI at around 3am, and transported to the Palm Beach County Jail. He is no longer at the jail.''
The 14-time major winner had been recovering from surgery after back spasms forced his withdrawal from the Dubai Desert Classic at the start of February.
He said in a statement last month: ''The surgery went well, and I'm optimistic this will relieve my back spasms and pain.
''When healed, I look forward to getting back to a normal life, playing with my kids, competing in professional golf and living without the pain I have been battling so long.''
Woods only returned to competition in December, after a 15-month absence through injury.
Plans to participate at Augusta in April, on the 20th anniversary of his first Masters victory, also had to be abandoned.
He last won a major in 2008, and in 2009 was charged with careless driving near his home after crashing into a tree and damaging a fire hydrant.
Woods later admitted to extra-marital affairs and made an apology in early 2010 in which he spoke of undergoing therapy, saying he was ''far short of perfect''.
In the blog discussing his surgery, he wrote last week that he ''hadn't felt this good in years'', but added: ''I'm not looking ahead. I can't twist for another two and a half to three months. Right now, my sole focus is rehab and doing what the doctors tell me. I am concentrating on short-term goals.''
