A 93-year-old woman will spend Christmas in hospital after being shoved to the ground by a stranger who was yelling abuse about old people.

The woman was shopping with her son in Melbourne's south-east when she was assaulted.

The injured grandmother in hospital on Wednesday. Credit:Twitter/@SebCostello9

Her son Neil told 3AW they were leaving Southland shopping centre in Cheltenham on Friday just before 11am when a woman walking towards them began screaming abuse at his mother.

"She looked up and started screaming about old people and looked at my mother and said, 'Old woman', and we thought, 'Well, we're going to walk around her.' And she turned and barged between us and pushed my mother over," he said.