The incident took place at Great Ormond Street Hospital
The 31-year-old man and 26-year-old woman arrived at the hospital in central London and told staff their child had been born at the nearby Royal London Hospital on March 1 and was transferred.
They allegedly showed staff a picture of their newborn baby in an incubator – thought to be a printout from the Internet – and claimed they had come to collect the child.
However staff alerted police after they contacted Royal London Hospital for premature babies and bosses found no records when they checked for children born on March 1.
Officers arrived at the scene and arrested the couple on suspicion of conspiracy to abduct a child.
The man and woman have now been released on bail on the condition that they should not enter any hospital – unless they are suffering a "medical emergency".
Inspector Paul Clarke, from the Metropolitan Police, said: "The actions of the staff at Great Ormond Street Hospital in making all of the necessary checks and the quick response of police in arresting a couple prevented what could have been a very frightening and harrowing incident."
A Great Ormond Street Hospital spokesman added: "Thankfully, this type of incident is exceptionally rare.
"We are pleased that staff at the hospital acted so swiftly and calmly to ensure the safety of all our patients."
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