"I want to apologise for the unwise choices I made over the weekend and for any inconvenience it caused my family, friends, business partners, the hotel and their guests," White said in a post on his Facebook page.
"I was celebrating a happy occasion with a ton of family and friends and got carried away. I'm truly sorry for my poor behaviour," he added.
The 26-year-old winner of gold medals at the 2006 and 2010 Winter Games did not specify what he was celebrating.
Nashville police said the chain of events that led to White's arrest began about 2am on Sunday, when officers responded to a call from the luxury Loews Vanderbilt Hotel that an intoxicated man had set off the fire alarm.
Police said a concerned bystander apparently kept White from fleeing in a cab and told the driver he was going to call police.
"When White overheard their conversation, he allegedly kicked the citizen and fled on foot," police said in a statement. "The citizen reported that he chased White until White turned and ran into him, apparently causing White to fall backwards and strike his head against a fence."
The citizen did not want to prosecute White for assault, police said.
"Responding officers Sunday reported that White appeared to be extremely intoxicated and smelled strongly of alcohol," the police statement said.
Police said White refused to sign misdemeanour citations, so arrest warrants charging him with vandalism and public intoxication were issued on Sunday morning.
White was taken to a hospital and treated for injuries after hitting the fence. He was released late on Monday afternoon, police said.
