A man has been charged after he allegedly punched a baby in the face at Central Railway Station in Sydney.

Police said the 16-month-old girl was in her pram with her parents outside a cafe on Eddy Avenue about 11.30am.

Officers will allege a 28-year-old man walked up to the pram and punched the baby in the face before running from the scene.

The baby's father began to chase the man and called out to bystanders to contact police, officers said.

The girl suffered a small cut to her face and was treated by paramedics at the scene.

The 28-year-old man was found in a nearby building on Pitt Street and was arrested and taken to Day Street Police Station.

He was charged with assault occasioning actual bodily harm and refused bail and was expected to appear before Central Local Court on Friday.

Acting Inspector Paul Hanna, who made the arrest, said the man did not appear to be drunk or on drugs.

"We systematically searched a number of buildings in that area and found him in an elevator," Acting Inspector Hanna said.

"I grabbed him out of the elevator. He was very quiet. He didn't appear to be affected by anything.

"He was quite unresponsive. I don't know how you explain that kind of behaviour and he didn't appear to be intoxicated."

Police praise bystanders for helping with arrest

Acting Inspector Hanna said when the man was questioned he did not explain why he punched the baby.

"I suppose he'll give those reasons to the court," he said.

"It's a bit of a puzzle really. It's not something we normally encounter."

Police said it was a quick arrest which was made possible by the help of bystanders.

"We were on scene within five minutes of the call and from memory it would have been within 15 or 20 minutes [that] we had him in the back of the truck," Acting Inspector Hanna said.

"It was a young girl who pointed us in the direction of Pitt Street eventually and helped us narrow it down eventually to where he'd gone to."

He said his team would spend the night preparing CCTV evidence for the court.

"The CCTV being what it is around Central railway, it's very high quality, and very well monitored by those guys so there'd be a fair amount of CCTV that we'll review and prepare a brief for the court tonight," Acting Inspector Hanna said.