The incident took place in the car park of St James Retail Park, near to Next, at around 5.15pm on Thursday.
North Yorkshire Police today said it was believed that the man had slapped the child across the face.
A spokeswoman said: "We are conducting enquiries and are requesting the public’s assistance to help us to identify the man and the boy and to determine the full circumstances surrounding the incident."
The man is described as white, aged in his mid to late 30s, of large build and approximately 5ft 9in. He had a stubbly beard and was wearing a beanie hat
The child, a boy aged around nine, had mousy brown hair and was wearing a school uniform. He is said to have been upset and scared at the time.
Anyone with information is asked to call 101, select option 2, and ask for Alex Langley.
Information can also be passed on anonymously via Crimestoppers on 0800 555 111.
Please quote the North Yorkshire Police reference number 12170015237.