The RSPCA is appealing for information after a member of the public heard a cat crying from inside the backpack and discovered the animal in the Hardane area of the city at around 2.30pm on Sunday, June 27.
RSPCA Inspector Thomas Hutton attended and collected the 12-week-old female kitten.
He said: "The caller explained that they heard the cat crying and when they opened the backpack they saw the small kitten inside wearing a pink collar.
"They also said the bag and the kitten smelt very strongly of smoke so possibly she has come from a home with smokers. The caller brought the cat home where she limped round and round in circles.
"I took her to the vets and sadly she continued her circling which made the vets believe she might have a neurological condition.
"After further tests, the little kitten stopped circling and the vets realised it was more like that she actually had a concussion from some sort of head trauma.
The animal charity is now warning people not just to abandon animals if they are struggling to look after them.
Mr Hutton said:“We know that people’s circumstances can change which may mean they can no longer care for their pets but there is no excuse to abandon an animal like this.
"This poor cat would have been confused and frightened and also possibly suffering from a trauma to the head and we don’t know at this stage if this happened before or after she was dumped."
Anyone with information is urged to contact the RSPCA on 0300123 8018.