Police are searching for a man who spat in the face of a four-month-old baby girl in Sydney in what officers described as a "despicable act".

The baby was being pushed in her pram by relatives on Crown Street, Surry Hills, about 5:30pm yesterday when the man, who was not known to the family, leant inside the pram and spat at the baby, before running off.

Surry Hills Police Inspector Mick Garrahy said the police were investigating the matter and did not have any indication what motivated the man's actions.

The baby's grandfather chased the man.

As he was running away he "collided with a motor vehicle". He got up and kept running south along Crown Street.

Inspector Garrahy could not confirm whether the man crashed into a parked car or was hit by a car.

"We will be speaking to the driver of the vehicle," he said.

Surry Hills police searched the area, but could not find him.

A police statement said officers would now like to speak with a man who may be able to assist them with inquiries.

He is described as being Caucasian, aged in his early 40s with a slim build and bald head and was last seen wearing a tie-dyed shirt and shorts.