This morning Family First spokesman Bob McCoskrie told the Herald he had written to the Crown and Little asking for a review of the sentence.
He said the sentence was "grossly inadequate".
"We would also call on the Crown to review and appeal this decision," he said.
The Herald asked police yesterday morning if they were considering an appeal.
A full response is yet to be received.
"Most New Zealanders will read about this sentence of just home detention and think that it is 'fake news' – a cruel joke," McCoskrie said in his letter.
"Yet it is the sad reality, and a weak and dangerous sentence for a shocking attack involving hospitalisation with lacerations around the baby's mouth, welts on both sides of his head, multiple cheekbone fractures, a torn bottom lip and tongue and facial grazes of a little 9-month-old.
"The offender also assaulted the baby's mother with a weapon.
"This was not a one-off event. The man had also assaulted the mother of his children on multiple occasions in 2015.
"The judge attempted to mitigate the horrendous offences by referring to his alcohol abuse and relationship difficulties by saying "that does not excuse your behaviour, but it provides context for it'."
McCoskrie said the judge should have considered only one context: "The message has to be clear – if you violently abuse a child, the full weight of the law will be used against you.
"Violent child abusers should not get a 'grounding' at home when the child victim gets a long-term sentence of both physical and emotional harm.
"This offender-friendly sentence sends a dangerous message and sets a dangerous precedent - we simply don't value the protection of vulnerable young children - based on the response of our justice system."
McCoskrie said the finger was "often pointed at communities to do more and speak up".
"But politicians and the legal system must also reflect the revulsion that New Zealand families have towards the violent murders of defenceless and vulnerable children," he said.
"The wrong message is being sent to society as to how much value is placed on the life of a child.
"This is just another example.
He called on the Crown to urgently appeal the sentence.
"People who murder and maim our children need to know that children will be afforded greater protection by the judiciary," he said.