Melanie Coleman fell during routine exercise on the uneven bars Friday, university spokesman Ken Sweeten said. She died Sunday.
"At this time, our thoughts and prayers are with Melanie's family," the university's athletic director Jay Moran said Monday. "This has been devastating to her coaches and teammates."
Coleman's longtime personal coach, Thomas Alberti, called the incident "a complete accident."
"It's just not something that anybody can process," he said.
Her family said she was the "light and love" of a large family.
"We are confident that her spirit, laughter, and humor will live on through the ones who loved her most, as well as through the gift of life to those who needed it most through organ donation.
While a death in gymnastics is extremely rare, it's happened before.
In 1988, 15-year-old Julissa Gomez became paralyzed after an accident on the vault. She died of complications from her injuries three years later.
And in the past 20 years, UPMC said, gymnasts have started the sport at earlier ages and are now performing more difficult skills.
Coleman, 20, was pursuing a degree in nursing. She also taught part-time at Alberti's gym, New Era Gymnastics.
"I was her full-time coach for 10 years," Alberti said. "She was always a leader at my gym. She was the leader that everyone looked up to."
Alberti said Coleman taught students ranging from ages 2 to 15.
Coleman came from a family of gymnasts. Her mother competed, as did her two older sisters.
"To her, it wasn't about trying to get a better score. What made her a great gymnast is also what made her a great person," Alberti said. "She had a desire to help everyone around her."
Jerry Nelson, who recently retired as head coach at Southern Connecticut State, said Coleman was a joy to those around her.
"Melanie was an extraordinary young lady that positively touched all that knew her," Nelson said in a statement. "Melanie was a true team player, a hard worker, and a true pleasure to coach."