At around 4pm on Thursday, the 78-year-old woman was robbed as she walked on Carmunnock Road, Castlemilk.
She was walking on the pavement near to the Co-op when she was approached from behind by a man who grabbed her bag (containing a small sum of money and personal items) causing her to fall to the ground.
He then ran off towards the shops at Croftfoot.
The woman was taken to the Victoria Infirmary where she was treated for injuries to her arm and hip before being allowed home.
The suspect is described as a white male, in his early twenties, 5ft 8 in height and has short dark hair.
He was wearing a navy blue hooded top and blue trousers.
Officers from the Robbery Unit at Pollok are continuing their enquiries and would like to speak to anyone who may have seen the suspect hanging around the Carmunnock Road area prior to this incident or anyone who may have seen him running off afterwards.