Officers are growing increasingly concerned for the welfare of Mark Henry Dallas from Chatham, who was last seen in the Wayfield Road area of the town just after midday on Friday.
It is believed the 19 year old was in possession of his 14-month-old son but the boy has since been found safe and well.
Mr Dallas is described as white, 5ft 11ins tall, of slim build, brown eyes and dark brown hair. He was last seen wearing a light grey tracksuit with a hood.
Kent Police is searching for Mr Dallas and officers are urging him to get in contact. Anyone who knows his whereabouts is urged to call 101.