The family said Van Dyken crashed her all-terrain vehicle on Friday night and was airlifted to an Arizona hospital to undergo surgery and was in good spirits.
"An amazing team of doctors performed emergency surgery to repair her spine and stabilize her," the statement said.
"Amy's spinal cord was completely severed at the T11 vertebrae, but, miraculously, a broken vertebrae stopped within millimetres of rupturing her aorta, and she did not suffer any head trauma.
"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 (Intensive Care Unit)."
Van Dyken's husband, former Denver Broncos punter Tom Rouen, was with her when the accident happened and comforted her while waiting for a helicopter to arrive.
''So hard hearing about (Amy) and her horrific accident,'' fellow American swimmer Missy Franklin said on Twitter. ''I am praying continually for you and your family.''
Rouen told police officers he had changed the throttle mechanism on the ATV from a thumb accelerator to a twist accelerator a few days before the accident, though he wasn't sure if it was a factor in the accident.
He said his wife had not been drinking alcohol that evening.
Van Dyken, 41, is one of the most decorated Olympic swimmers of all time, winning six gold medals during her glittering career in the pool.
At the 1996 Atlanta Olympics, she won the 50 metres freestyle and 100m butterfly as well as winning two relay golds for the United States. She won another two gold medals in relays at the 2000 Sydney Olympics.
"The USA Swimming family is devastated to learn of Amy Van Dyken's unfortunate accident this weekend. We're happy to hear that she escaped and is now in great care," USA Swimming said in a statement.
"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."
- Sports & Recreation
- Amy Van Dyken