The magazines had general titles that suggested links with worthy causes like road safety, parenting or drug addiction.
The SFO alleges the invoice scam generated up to $1.6m since 2008.
The arrests come at the conclusion of Operation Edit, which involved staff from police, the SFO, the Organised and Financial Crime Agency, Customs, Inland Revenue and the Commerce Commission.
The operation involved covert investigations, detailed analysis of banking records and numerous victim interviews.
Acting SFO chief executive Simon McArley said high-volume, low-value fraud was particularly difficult to address.
But the operation was completed in a relatively short timeframe because of the multi-agency approach.
"The agencies were able to each contribute specialist skills and achieve a result that none working alone would have been able to," Mr McArley said.
"Invoicing scams cost New Zealand businesses hundreds of thousands of dollars a year and small businesses and charities are often the target.
"While the dollar amount of alleged offending is not huge, taking action in relation to high-volume, low-value fraud is important. Overall there can be a significant impact on the economy."
The SFO will take the lead responsibility in prosecuting the case.