The incident happened at around 9.55am on Wednesday 27 August 2014 at the pelican crossing on the junction of Lendal Bridge and Station Avenue.
The baby was walking with her childminder and an assistant when she began to cry. On hearing her cry, a man who was stood in front of them, has unexpectedly turned around, walked a couple of paces and kicked the baby in her stomach. She suffered a minor external injury as a result of the incident.
A woman who was with the man, immediately apologised for the incident explaining that the man had a behavioural condition.
Police are appealing for the man and woman to come forward and to anyone who witnessed the incident to contact them.
The man is described as aged between 20 and 35, of heavy build, approximately 5ft 6in tall and with thin hair. He was wearing dark coloured trousers and an older style jumper with stripes. His shoes are described as big and he appeared to be dressed in clothing which an older person would wear.
The woman who accompanied him is described as around 5ft 6in tall, aged in her early twenties, of slim build with dark hair.
Witnesses to the incident, the woman who was with the man, or anyone who can help identify them, are asked to contact the police as soon as possible.
Please contact North Yorkshire Police on 101, select option 2 and ask for PC Craig Appleby. Or email firstname.lastname@example.org
If you prefer to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote reference 12140146357 when passing on information about this incident.