The 19-year-old, who won four golds at last year's World Championships in Glasgow, has a progressive neurological condition which causes muscle weakness.
"A recent progression in my condition, coupled with an ongoing shoulder injury, has affected my ability to train," she said.
"I did everything in my power to get to Rio, but it just wasn't to be."
The Paralympics begin on 7 September, while the swimming events run from 8-17 September.
Kearney, who has been battling to be fit since the start of the year, missed the British Paralympic swimming trials in April but was named in the team in May.
She added: "I'm devastated not to be able to represent GB in Rio.  I have worked incredibly hard in training for many years to get to this point in my career and last year was fantastic for me.
"Obviously, I hope that there will be a way for me to continue to compete in the sport I love so much next season and beyond."
British Para-swimming national performance director Chris Furber said: "We all share in Tully's disappointment in this news.
"As a team we worked closely with Tully to ensure she had the right support and as much time as possible.
"Our whole medical and coaching team has and will continue to provide the best support possible for Tully. We all wish her a speedy return to competition."
Swimmer Tully Kearney has had to withdraw from the Great Britain team for the Rio Paralympics through injury.