Adrian Brookes, 36, had admitted wasting police time at the height of the search by claiming he knew where Abbie was.
But Roy Anderson, a Nottingham stipendiary magistrate, told him his behaviour had been 'wicked, calculating and quite deliberate'. The matter could be dealt with only by a custodial sentence.
Before he was led away from the dock in handcuffs, Brookes told the court: 'I am absolutely disgusted with myself for the pain I have caused to Mr and Mrs Humphries. I am absolutely ashamed of myself and I am extremely sorry.'
Brookes, of Matson, Gloucestershire, called himself 'Gary' in a series of calls that started four days after Abbie was snatched from the Queen's Medical Centre in Nottingham on 1 July, just four hours after her birth.
Russell King, for the prosecution, told the court that Brookes's malicious calls had seriously hampered the police investigation.
Detectives estimated the inquiry was delayed by two or three days. Nottinghamshire police lost 225 man hours and 35 Gloucestershire officers used up a further 593 hours on surveillance and tracking operations.
Brookes had originally faced two charges of causing grievous bodily harm to Abbie's parents, Roger Humphries, 33, and his wife, Karen, 32. But this was later reduced to one charge of wasting police time.
Mr King said the television presenter John Stalker, the former deputy chief constable of Manchester, had received the first calls within hours of a television appeal for Abbie's return on 5 July.
'Gary' had claimed his wife had taken the baby and he wanted Abbie's parents to know she was safe and well. He said his wife had lost a baby 12 months earlier and was desperate for a child.
In further calls, 'Gary' said he would return Abbie to a police station but then hung up. Mr King said the calls had been traced and Brookes had been arrested at Gloucester County Court where he was appearing at a family hearing.
At first Brookes had denied the offence, telling police that he had allowed two hitchhikers to stay at his home and suggesting that they were responsible.