"It's embarrassing for Tiger, something that you can't go back and change", Begay said on Golf Channel from the NCAA men's golf championship in Sugar Grove, Illinois, where he was working for the network.
He faces a charge of driving with a blood alcohol level above Florida's legal limit of.08.
The arrest is the latest gloomy episode to embroil Woods, who once towered over his sport before being engulfed by turmoil in his private life and a series of debilitating injuries.
He was then released from Palm Beach County Jail at 10.30am.
The 14-time major champion and victor of 79 PGA Tour titles has not played since he withdrew from the Dubai Desert Classic on February 3 after an opening-round 73.
Ms Rightler said she did not have additional details about the circumstances leading to Woods's arrest, nor did she have any information about whether the arrest involved drugs or alcohol. He has played only three times in the last two year. Last month, Woods announced that he had undergone his fourth back surgery since 2014.
The 14-time major victor had been recovering from surgery after back spasms forced his withdrawal from the Dubai Desert Classic at the start of February. "We tried every possible non-surgical route and nothing worked", he added. "I had nerve pain with anything I did and was at the end of my rope".
Woods also said in the post that his long-term prognosis for returning to professional golf is positive, but that he won't be able to twist his back for another two to three months. Soon after that meeting, the Golden Bear said he spoke to an acquaintance (Nicklaus wouldn't say who), who said of Woods, "He won't be back".
"I want to play professional golf again but I'm not looking ahead", he said.