"It's important Kiwis recognise that by buying fake product they're not supporting their favourite team, quite the opposite," he said. "They're impacting the deals that help grow the sport."
New Zealand Rugby's deal with adidas is estimated to be worth at least $10 million a year.
Bleakley said the company was "very familiar" with websites offering very cheap All Black branded gear.
"There's a reason why it's cheap, the quality of fake goods is always poor and leaves Kiwis ultimately disappointed," he said.
The sales of rip-offs was "a reoccurring problem that seems to become more prolific as a World Cup year rolls around", Bleakley added.
He said adidas was "experienced in protecting our rights" and took "appropriate action" when made aware of breaches of their trademarks or rights.
"While we couldn't comment on individual legal disputes, it is fair to say such action is taken when required."
NZ Rugby chief commercial officer Richard Thomas said "sadly it's not a new behaviour to have unscrupulous operators trying to leverage our brand and those of our sponsor partners, to peddle their fake products".
"We also know that our partners pride themselves in the quality of their products," he said.
He urged fans to buy authentic product from "large-scale retailers".
And the Warriors have also been targeted by another Chinese-based website, with a full range of fakes based on the club's new-look 2019 playing strips.
Warriors boss Cameron George said the makers of the gear were ripping off the club's identity.
He would be reporting the fakes – which cost $26, compared to $170 for the real thing produced by Canterbury of New Zealand – to the NRL who would take action; which would could potentially include seeking the shirts being taken down.
"The NRL are normally pretty good at sorting it out," he said.
"[But] a lot of the time it is often hard to shut them down – they just pop up down the track somewhere else."
George said the counterfeit items were being produced by people "looking for a cheap way to make money".
"The people who do this stuff ... all the hard work [around reputation and branding] is done elsewhere," he said.
"[Branding] is a huge part of our business ... it is absolutely everything. It is the integrity of the product. The people who start to rip off [our identity] impacts on the integrity.
George said the money received from its authentic gear was hugely important; unlike many other clubs in the NRL the Warriors did not have an associated gaming club which generated money via pokie machines.
A spokesman for the NRL said it was "aware there are knock-off products in the market and we try and combat these where we can".
He said that was a "difficult task", but wouldn't elaborate on what steps it could take on "counterfeit product".
Canterbury of New Zealand did not respond to a request for comment.
Consumer New Zealand chief executive Sue Chetwin said people who purchased the counterfeit items would have no protection under our consumer laws if they were substandard.
She believed those that bought the cheap items would be aware they were fake, adding NZ Rugby and the NRL would obviously be "disappointed" at how easy it was to purchase them.
"I guess they will have to ask [themselves questions over] the price for the official and profit margins," Chetwin said.
"If you are family of five or six living in South Auckland and waiting to deck themselves out to go and support the All Blacks or Warriors, the fake jerseys are an appealing option."
The rise of the fakes was slammed by former All Black captain and ex-New Zealand Rugby Union president Andy Leslie.
Leslie – who also previously co-owned a clothing store – said those producing the fakes were "ripping off the system. It is terribly sad."
"The likes of adidas pay sporting bodies a lot of money to sponsor the team [and produce official replicas]," he said.
When asked for his feelings on the fakers, Leslie said: "They should be hung drawn and quartered."
The Tobeno1 shop – which is selling the knock-off All Black, Māori All Blacks and Super Rugby jerseys – did not respond to a request for comment.
The Warriors jerseys come with the brand Yigege and are sold on the Chinese-based AliExpress website.
The Herald on Sunday could find no contacts for Yigege.
Questions sent to AliXpress – which has the motto "We have your back" on its website – went unanswered.
