The player, who was charged with Driving Under the Influence (DUI), blamed “an unexpected reaction to prescribed medication”.
“I understand the severity of what I did and I take full responsibility for my actions,” he said.
Police released a mugshot of Woods, looking unshaven and unkempt, following his arrest in the town of Jupiter.
“I want the public to know that alcohol was not involved. What happened was an unexpected reaction to prescribed medications,” he said.
“I didn’t realise the mix of medications had affected me so strongly.”
He added: “I would like to apologise with all my heart to my family, friends and the fans. I expect more from myself too.”
Police records show the 41-year-old golfer was pulled over at about 03:00 local time (07:00 GMT) near his home in Jupiter and later taken into custody. He was released from Palm Beach County jail at 10:30 local time.
The record says that he was released “on his own recognisance”, meaning he promised in writing to co-operate with future legal proceedings.
Woods has been recovering from back surgery. In his most recent comment about his health, he wrote that the surgery had relieved terrible pain and that he hadn’t “felt this good in years”.
The 14-time major champion’s personal life came under scrutiny in 2009 when he was charged with careless driving outside his Florida home.
He later admitted to having had extra-marital affairs and made a frank public apology. He said he had received professional help and planned to undergo further therapy.
The golfer lost several sponsors over the scandal and took a break from competitive competition.