After a short appearance, he was remanded in custody without plea to appear in the High Court on February 18.
At the request of defence counsel Kerry Cook, Judge Couch granted interim suppression of name until the High Court appearance.
Cook said continued suppression would be argued at the next appearance and the man would make a bail application then.
Judge Couch also granted suppression of the name of the child's mother "until further decision of the court".
At the request of police prosecutor Glenn Henderson, Judge Couch also granted interim suppression of the name of the child.
The man faced a charge of drink-driving, which will continue to be dealt with in the district court.
"Police extends its deepest sympathies to the child's whānau," a short police statement said.
"The family have requested privacy at this time.
"The investigation is ongoing and police are not in a position to release the child's name or provide any further comment at this stage."