Maisha Ahmed Mohamed, 22, of Wray Gardens, Levenshulme, said she thought she had suffered a miscarriage six weeks before she was due to give birth.
But when questioned she claimed the baby boy had been stillborn in Liverpool and she put him in a bin.
Police have never been able to trace what happened to the baby's body.
Detectives said this was the first time anyone had been sentenced for child destruction in Greater Manchester.
During questioning, police said Mrs Mohamed gave various accounts of how and when she had come to lose the baby, as well as what had happened to the remains following the miscarriage.
The judge Justice McKinnon said the true circumstances of the baby's death would remain a mystery.
He agreed with police investigating the case that she almost certainly asked an illegal abortionist to get rid of the foetus, when she was already seven-and-a-half months pregnant.
Det Insp Brian King from Longsight CID said: "This was an extremely distressing case for everyone involved.
"Throughout the course of the investigation, Maisha has consistently lied about what happened to her baby and has shown little remorse for what she did.
"We may never really know what happened to this child or Maisha's real reasons for doing what she did."
