Van Dyken Rouen, who is married to former NFL punter Tom Rouen, was launched over a curb while driving the ATV in a parking lot on Friday night and lost feeling in her legs, according to several reports.
She was airlifted to a Scottsdale hospital and underwent emergency surgery to repair her spine and stabilize her, according to a letter from the Van Dyken and Rouen families posted online by Swimming World magazine.
The letter says the broken vertebrae "stopped within millimeters of rupturing her aorta, and she did not suffer any head trauma." It says her husband "kept her stable" at the scene until a helicopter arrived.
"Amy awoke within hours of surgery acting like her typical spunky, boisterous, ebullient self and has spent the last 24 hours entertaining her family and her medical staff in the ICU," the family said.
"She has made at least one male nurse blush. Amy's attitude has been overwhelmingly positive and optimistic. She has been far more of a comfort to us than we have been to her.
"Amy has a long, trying road ahead of her, but as anyone who knows her can attest, her unparalleled mental strength and determination will propel her. She is a fighter. Amy has overcome seemingly insurmountable obstacles before, winning 6 Olympic gold medals and becoming one of the greatest female athletes of her generation despite battling lifelong chronic asthma.
"Now this is her new challenge, her new battle. With the unconditional love and support of her friends, family and fans, Amy welcomes the challenges she will face as she opens this new chapter of her life."
Swimming as Amy Van Dyken, she became a star while winning four gold medals at the 1996 Atlanta Olympics -- in the 50-meter freestyle, the 100 butterfly and as part of two relay teams. She won two more relay gold medals four years later at the Sydney Games.
USA Swimming said in a statement it was "devastated" to learn of Van Dyken Rouen's accident.
"We're happy to hear that she escaped and is now in great care. That she is already 'acting like her typical spunky, boisterous, ebullient self' shows she's on a great path," the organization said.
"Amy is a champion who has proven throughout her life that she is a fighter who takes on challenges and comes out on top. We know Amy will tackle her rehabilitation with vigor and be back on her feet sooner rather than later."