It jumped on her back and tore her coat with her claws and teeth.
Only drivers hooting their horns scared the wild animal away, and stopped the puma badly wounding her.
She ran into a nearby car to take refuge.
A video shows the puma jumping through flames during a performance in the circus.
Diana, 15, said: “My mother and stepfather noticed the puma. A girl was buying tickets for next performance, and my family was about to queue behind her when they saw a huge cat.
“That second the puma jumped on the girl’s back from behind and tore her winter coat. We all screamed and the cat retreated.
“My parents sat the girl in our car. The puma wasn’t too big, it was a young animal.”
The victim has not been identified.
But it was reported she was not wounded thanks to wearing a thick coat.
“If the attack had been in summer, she could have been badly mauled,” said a witness.
The Dovgalyuk Dynasty circus has apologised for the attack, and said the puma was caught and returned to its cage within an hour.
It was reported the circus offered an out of court settlement to the woman and she agreed, reported The Siberian Times.