Emma Tustin, the boy's stepmother, was sentenced to at least 29 years in prison for her murder. Thomas Hughes was sentenced to 21 years for manslaughter.
Suella Braverman's office stated that the sentences have been referred to Court of Appeal.
Six-year old Arthur, from Solihull, died after suffering a fatal brain injury. He had been tortured and poisoned.
The court hearing date is still to be determined.
During the couple's trial, Arthur was accused of being poisoned with salt and subject to frequent beatings. He was also denied food and drink, and forced to stand alone for hours in the hallway.
Ms. Braverman stated that she had carefully considered the facts of the case and concluded that the sentences were "too low".
