Police say up to $100,000 may have been stolen from some victims after access was gained to their bank accounts.
They say police and Ministry of Internal Affairs staff joined forces on "a significant cybercrime operation" which began in 2022.
Two men were arrested in central Auckland on Wednesday.
"Police executed a search warrant at an address where the two men, who are UK-nationals, were arrested without incident," Detective Senior Sergeant Craig Bolton said.
"A number of laptops, phones, SIM cards, and electronics police allege are consistent with running a fraudulent text message scam were also located at the address."
The two men, aged 18 and 19, are facing 22 charges and have appeared in the Auckland District Court.
Bolton, of the Auckland City Financial Crime Unit, said police allege the scam had been circulating among Kiwis' messages since November 2022, however, it escalated significantly in 2023.
"The text messages were impersonating well-known and trusted establishments and asking the public to provide their personal details.
"It's estimated those involved had scammed some victims out of between $10,000-$100,000 after gaining access and control of their bank accounts."
Bolton said the 19-year-old has been remanded in custody.
He suspected others were involved and was not ruling out more arrests.
"We hope these arrests serve as a warning to potential scammers that New Zealand authorities will not tolerate this scam.
"Police and our partner agencies are committed to holding those who choose to engage in this type of offending to account.
A year's work
Manager digital messaging and systems at the Ministry of Internal Affairs (DIA) Joe Teo said these arrests were the result of a year's worth of cross-organisation collaboration from DIA, police, customs, CERT NZ, New Zealand telecommunications providers and banks to combat the rise in scams in Aotearoa.
"Through a joint effort we have identified and targeted multiple New Zealand and overseas nationals propagating the majority of scam messages in 2023 and exploiting our telecommunications infrastructure," he said.
He said the operation showed the value of cooperating "to stop scammers in their tracks".
Police continue to ask the public to be vigilant when it comes to providing your personal information.
"Legitimate businesses will never call or text customers seeking confidential information," Bolton said.
"Always be suspicious when you receive such requests.
"Scammers will often pretend to be from a known, or reputable, agency or business so even if it appears to be someone you regularly deal with, the safer option is to independently log into that company's website to check your account," he said.
People need to be cautious about clicking links in texts or email.
"The scammers are powerless if you don't play into their hands."
Scams can be reported to police via the 105 phone service or anonymously via Crime Stoppers on 0800 555 111.
DIA has a text spam reporting service which collects reports on malicious scams and spam.
Anyone who receives a suspicious text message can forward the message to 7726 for free.
RNZ
