The passing cyclist kicked the 19-month-old child as she was walking with her father by the cycle path near Leith Links on Saturday afternoon.
The pair had moved out of the way to let the man by on his mountain bike, however he kicked the little girl as he cycled past at around 4.30pm.
The suspect is described a white man in his mid 20s and of medium build.
He was clean-shaven with dark scruffy hair and dark circles under his eyes. He was wearing dark jeans and a black hooded jacket.
Sergeant Mark Wilson of Leith Police Station said: “Thankfully the child was not seriously injured but this was still a distressing and inexplicable incident.
“We are keen to speak to anyone with information that can help us with our inquiries and assist us to trace this suspect.
“Anyone with information can contact us on 101 or anonymously via Crimestoppers on 0800 555 111.”