"The chairman will look at the billboard and the complaints and make a decision whether it comes under our jurisdiction," she said. "It most likely is, we just need to confirm that."
The authority would take about 25 days to process the complaint.
Jody Condin, who initially submitted a complaint, said she was pleased the authority was investigating.
"I'd be happy if they at least looked into it, if they found that there was no wrong doing, [then] so be it."
Consumer NZ chief executive Sue Chetwin said from a consumer's position the billboard "falls between the cracks", as a church does not come under the Fair Trading Act.
But she was hesitant to advocate a type of control system, despite acknowledging the billboard could be hurtful.
"Do we want regulations for this sort of thing? A sensible person would probably ignore it."
The Ministry of Consumer Affairs also said the billboard did not fall under its jurisdiction as a church was not covered by the Fair Trading Act.
Senior Minister Lyle Penisular was not available today for comment.