Tidd hasn't trained since the 2005 NCAA Championships because of lower back problems. A junior, Tidd was third on the bars and 12th in the all-around last year at nationals.
Tidd spent some time in California undergoing a variety of treatments, but nothing has helped.
"While I have realized that this was the likely outcome for some time now, it was important to me that Rachel felt it was her decision to make," Utah coach Greg Marsden said. "She is a talented athlete, a great student and a wonderful person. Although we miss her presence in the gym, I believe this decision is best for Rachel's long-term health."