A middle-aged man spat in a baby's face and then ran off only to be hit by a car in a bizarre unprovoked incident in an inner Sydney street.

The four-month-old child was being pushed in a stroller on Crown Street in the inner Sydney suburb of Surry Hills about 5.30pm on Saturday when the man leant inside the pram and spat, police said.

The child's grandfather then chased the man who ran away but collided with a car on nearby Foveaux Street.

The man got up and ran off again and was last seen heading south along Crown Street, a police spokesman said.

Police conducted patrols of the area but were unable to locate any trace of the man who is described as Caucasian, aged in his early 40s, with a slim build and bald head and was last seen wearing a tie-dyed shirt and shorts.