The man was pictured in the Barton Arcade, Manchester, at 2.30pm on Sunday with a baby in a pram.
The image, which was shared with the public by Greater Manchester Police, was snapped after the man allegedly tried to sell the baby.
Sergeant David Henshall appealed for eyewitnesses to come forward, saying: “This is extremely unusual and at this time we are trying to establish the full circumstances of the situation, but most importantly check on the welfare of the child.
“If anyone recognises the man in the image or has been approached by him in a similar situation please contact police urgently.”
Now, thanks to information from members of the public, police have arrested a 28-year-old man on suspicion of neglect.
He remains in police custody for questioning.
Police officers also confirmed that a three-month-old baby girl has been found safe and well.
DI Liam Boden of Greater Manchester police said: “We would like to thank members of the public and the media for their assistance in publicising the appeal earlier today.
“We have now arrested a man on suspicion of child neglect and will be questioning him in relation to the incident as we try to establish the full circumstances.”