The woman, who cannot be named for legal reasons, admitted causing grievous bodily harm to the baby in August 2014.
She will serve seven and a half months in prison and the same time on supervised licence.
A judge said the child had since been taken into care and had lost the chance of a normal upbringing.
He added that the woman had breached her trust as a mother and said the force needed to cause the injures was considerable.
The judge said that if the woman had any further children it was likely they too would not be left in her control.
At a previous court hearing, a prosecutor said police were called to the woman's house by social services after she had alerted the authorities to marks on her son's body.
She said she was concerned she may have caused the marks and injured her son by the way she was holding him while he was crying the day before.
The baby was brought to hospital where he was found to have extensive bruising to his abdomen. When an X-Ray was done, it showed three separate rib fractures.
Belfast Crown Court was told the injuries were "non-accidental".
When the child's mother was interviewed by police, she said her son had been crying and she was trying to comfort him.
She also told police she waited until the following day to alert the authorities because she knew her baby would be taken from her and she could not face the prospect of losing him.
A defence barrister said that while his client never denied she was responsible for causing her son's injuries, she never intended it to happen.
The barrister told the court there were no signs of neglect, adding: "Her remorse is enormous and continuing. She will have to live with this for the rest of her life - that child will not be granted back to her custody."
A 35-year old south Belfast woman who fractured three of her four-week-old son's ribs has been jailed.