The incident took place near Grove Road Primary School on Skipton Road between 10.20am to 10.30am on Wednesday July 21.
The woman assaulted a three-year-old girl who was in a pushchair and accompanied by her mother after stopping to speak to them.
The suspect is believed to have grabbed the girl whilst she was still in the buggy and pinched her ear, causing fluid to appear, before striking her on the head three times.
The child did not require medical attention.
North Yorkshire Police are appealing to anyone who was on Skipton Road at the time who witnessed the incident or any motorists who may have captured it on a dashcam to come forward.
The woman is described as being white, of a 'chubby' build, aged between 40-50 years old, and with short brown hair. She was wearing dark glasses and a short sleeved pink T-shirt.
Anyone with information that could assist the investigation is asked to email [email protected]rthyorkshire.police.uk or call North Yorkshire Police on 101, quoting incident number 12210164772.