The child, who can only be identified as "M," has been in a coma since being brought to hospital in May.
Her parents have been charged with beating and starving the girl, and are currently being held in custody.
On Wednesday, the Alberta Court of Appeal upheld a lower court ruling that ordered the girl be taken off life-support as soon as "reasonably possible."
The court also refused to grant a stay of the order pending an appeal to the Supreme Court, stating there were no grounds to take the case to Canada's top court.
On Thursday morning, April Kellett, the lawyer acting on behalf of the child's mother, filed a motion with the Supreme Court of Canada to keep the girl on life-support .
The Supreme Court has confirmed that the motion was dismissed.
Previously, the girl's doctors said she was highly unlikely to survive once taken off life-support.
Child found starving, in cardiac arrest
Paramedics were called to the family's home in May where they found the child with a head injury and in cardiac arrest.
Both the girl and her twin sister were severely malnourished.
While her sister is recovering, doctors said M's brain damage is so severe that she will never regain consciousness.
The child's parents are being held in jail, facing charges of aggravated assault, criminal negligence causing bodily harm and failing to provide the necessities of life.
None of those allegations have been proven in court.