"I sped up, and in an effort to elude an oncoming car which was making an illegal U-turn, saw no choice but to drop my bike," the 39-year-old country singer said.
"In actual fact, my pursuer came to my assistance, without taking photos, and helped me from the road," Urban said. "I returned home, got my car, and continued on my way."
Urban said the incident was the result of "one person's desire to do his job and my desire to maintain my privacy."
The New Zealand-born Urban, who grew up in Australia, completed a three-month stint in rehab for alcohol abuse earlier this year.
He checked himself into the Betty Ford Center in Rancho Mirage, Calif., last October, less than four months after his wedding to Nicole Kidman.
The couple have a home in Nashville.
Keith Urban was uninjured Monday when he crashed his motorcycle near his home in Sydney, Australia.