Wayne Jackson, 35, walked into Holbeck police station in Leeds at 7pm on Saturday night and handed Chloe - his daughter by an earlier marriage - to officers at the front counter.
He told them he couldn't look after her, left a telephone number and walked out.
Mr Jackson did not say he was the child's father but the number he left was that of her grandmother, Janet Atha, 46. Mrs Atha recently underwent surgery and had been unable to babysit as usual on Saturday while her daughter Gayle Atha, 24, the child's mother, worked.
Police reunited the child with her grandmother within an hour .
Gayle Atha, who split up with Mr Jackson shortly after their daughter's birth, said: "I am absolutely distraught that he can't even care about his own child. I never expected anything like this from him. I can't believe he would dump her at a police station. He was unreliable but at the end of the day I thought he loved Chloe."
Janet Atha, who is still recovering from a major operation, said: "We're absolutely astounded ... I mean, you don't treat an animal like that; she's not something you hand in to the RSPCA."
She said of her daughter: "She is so upset about it all, she just doesn't know what to do. How can someone behave like this?"
West Yorkshire Police are considering whether to bring action against Mr Jackson, who lives in the Halton area of Leeds and is reported to have left the country with his wife and other children for a wedding anniversary celebration.
Inspector Mick Starkey said: "We can confirm that a 35-year-old man left his baby daughter with officers at Holbeck police station, saying he was going on holiday. [Chloe] was reunited with her grandmother within an hour and is fit and well. Social services have been informed of the situation and we are now looking into the circumstances."
The police said the case had been referred to the child protection unit and social services staff in Leeds, and that both were investigating the circumstances of the case. Mr Jackson was likely to be questioned on his return to Britain, a spokesman added.
A spokesman for Leeds City Council said: "We are aware of the incident and are currently in the process of gathering more information about it. We can't comment further until this process is complete and we have decided on the most appropriate course of action."
Neighbours of Mr Jackson, who runs Majestic Charity Care in Meanwood, Leeds, said yesterday the family had gone on holiday to Spain.
r Bristol police yesterday appealed to a mother who abandoned her days-old baby boy at a city hospital to contact the Bristol Children's Hospital, where the baby is being cared for. The youngster, who is three to four days old, was left in a toilet at the hospital on Sunday.Reuse content