A three-year-old boy was left with a cut lip and swelling to his face after a stranger allegedly approached the child's pram and kicked him in the face in the city on Friday night.

Police have arrested and charged an 18-year-old man over the incident, that resulted in the toddler needing treatment at Sydney Eye Hospital.

The teenager allegedly approached the boy's parents as they pushed their son along King Street about 11.30pm.

The man, who was unknown to the family, made repeated "demands" to the couple, police say.