The Martin County Sheriff's Office said the 15-time major champion was also charged with property damage and refusal to submit to a lawful test.
Woods, 50, rolled his Land Rover after clipping a pressure cleaner truck while trying to overtake it at "a high rate of speed", according to Sheriff John Budensiek.
The golfer, who had to crawl out of the passenger door of his vehicle, passed a breathalyser test after the crash but refused a urine test.
No-one sustained any injuries in the incident which took place on Beach Road in Jupiter Island just before 14:00 local time on Friday (about 19:00 GMT).
Sheriff Budensiek told a news conference: "The DUI investigators came to the scene and Mr Woods did exemplify signs of impairment.
"They did several tests on him. He did explain the injuries and surgeries that he's had and we did take that into account, but they did some in-depth roadside tests.
"When it was determined, he was placed under arrest and taken to the Martin County jail.
"At the Martin County jail, and even on scene, we were really not suspicious of alcohol being involved in this case and that proved to be true.
"Mr Woods did a breathalyser test with triple zeros, but when it came time for us to ask for a urinary analysis test, he refused."
Budensiek also said Woods had been "co-operative but was trying not to incriminate himself".
"He has a right to refuse that test," added the sheriff. "There is a statute which he will be charged with for refusing to take that test, but we will never get definitive results as to what he was impaired on at the time of the crash."
US president Donald Trump was asked about the crash on Friday, saying: "I feel so badly. [Woods has] got some difficulty. There was an accident. That's all I know.
"He's a very close friend of mine, he's an amazing person, an amazing man."
Sheriff Budensiek said Woods would remain in jail for eight hours then be released on bond. The charges are misdemeanours, not felonies.
