The California Highway Patrol says Ryan's 1995 Jeep Wrangler went off the side of Pacific Coast Highway near Malibu and landed on its roof Monday afternoon.
Besides Montag, Ryan's celebrity clientele included musician Vince Neil, actor Lorenzo Lamas, reality stars Lisa Gastineau and Adrianne Curry and several models and beauty queens.
Montag, who underwent 10 procedures in one day with Ryan, took to Twitter to share her reaction to his death.
"I am devastated," the 23-year-old wrote on the micro-blogging site Tuesday. "He was the most amazing person I have ever known. He was an angel and changed my life and the lives of everyone he met. He was the most brilliant talented surgeon who will ever exist. Dr. Frank Ryan changed the world."
The Ventura County medical examiner's office said an autopsy would be performed Tuesday. He said no cause of death has been established.
Ryan's friend and client, model and reality star Janice Dickinson, was "deeply, deeply anguished" after hearing of the doctor's death, her publicist said.
"She is stunned and wants the world to know what a genius Dr. Ryan was," publicist Brad Taylor said Tuesday. "Her love goes out to his mother and the rest of the family."
Curry said in a statement Tuesday that she and Ryan shared "in-depth conversations about him wanting to start a family of his own, now that he had a very successful career."
Ryan operated on her twice, she said, adding, "I considered him a friend."
According to his website, Ryan graduated from the University of Michigan in 1982 and from the Ohio State University College of Medicine four years later.
Ryan opened his private practice in 1994, the same year he established his namesake charitable foundation that provides free removal of gang-related tattoos and hosts day and overnight camps for children at Malibu's Bony Pony Ranch.
Ryan is survived by his mother, Mary Kate Ryan, and by many cousins, aunts and uncles, according to estate representative Melanie Sims Frank.
His family is grieving and asks for privacy, she said, adding that a candlelight vigil will be held at 7:30 p.m. Tuesday at Malibu's Zuma Beach.