Police said it was reported that a woman had approached a baby in a pram on Central Drive, near to the Coral Island amusement arcade in the Lancashire seaside town, at around 11.55am on Saturday.
Members of the public and the baby’s parent intervened, Blackpool Police said, adding the baby was unharmed.
A 51-year-old woman has been arrested on suspicion of child abduction and police assault.
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Enquiries are ongoing and the force has advised people to avoid speculating about the incident online.
Chief Inspector John Jennings-Wharton said: “We know that something like this can be very concerning for the community to hear about.
“We are in the early stages of our investigation and are working to establish the full circumstances.”
He added: “If you do have information or footage that could assist those enquiries, we ask you report them to us through the appropriate channels.”
