The 28-year-old man found the baby outside his home in the northern port city of Rostock late on Wednesday after answering his door.
The baby boy he found there was only about five hours old but was healthy, a police spokesman said. The mother had seemingly given birth to him without any medical supervision, as the umbilical cord had not been professionally cut.
Although in a film, the young man would keep the baby and try to find the mother, in real life both of these tasks have been taken on by the authorities.
The state prosecutor which is checking to see if a crime had been committed, said there was nothing to suggest a link between the man on whose doorstep the baby was deposited, and the child.
Because the baby was not put in any immediate danger, it would not seem that his mother committed a crime, a prosecutor spokesman said.
Sniffer dogs were brought in immediately to try to trace the mother's scent from the doorstep, but without success.
The baby, who has been named Florian by nurses at the hospital where he was taken, was immediately put into the care of the local social services, Die Welt newspaper reported on Thursday.
When left on the doorstep, he was wrapped in a yellow baby sleeping bag which bore the words, “Born in Rostock South Hospital” – such sleeping bags were given out to new mothers who had baby there late last year. They were only handed out for a short period of time, and it is thought Florian's mother may have got hold of one from a friend or acquaintance.
Within that he was wrapped in two woollen blankets, one orange, one beige. He was also dressed in a pink and white striped long-sleeved sleep suit.
Police are appealing for information from the public to trace the mother.