Australian police have arrested a man after he allegedly punched a baby girl in the face outside Sydney Central train station in an apparently random attack.

Police have charged a 28-year-old man with assault causing bodily harm. He purportedly approached the baby girl as she sat in her pram on Eddy Avenue and punched her in the face.

The suspect then ran from the scene as the father of the baby tried to chase him down.

The parent also shouted for bystanders to call for police while he was in pursuit.

Police found the man at a nearby building on Pitt Street and arrested him. He was charged and refused bail. He is expected to appear at Central Local Court on 19 June.

Paramedics treated the baby at the scene for a minor cut.