The incident at Main Street in Markethill is said to have happened at around 12.15pm on Monday afternoon.
Police in Armagh said: “It’s reported a lady 50-60 years old wearing a blue fleece puffa jacket, blue trousers, black rimmed spectacles, and had mid length black hair, dragged and struck a young child around 3-4 years old wearing a grey jacket white trousers and a red hat.
“We know that a number of people seen this incident, and would would ask that anyone with information who can help us identify the female and child contact us on 101 quoting ref 576 5/3/18.
“Most important thing is that we can check on the welfare of the child.
“We need to protect our children, whether they are yours or not.”
Police said enquiries are ongoing to identify the woman and child involved and officers would ask anyone who witnessed the incident or who has any information which could assist them with their enquiries to contact Armagh police on 101 quoting reference number 576 05/03/18.