Those investments are just a tiny slice of the $100 million of shares the fund has in a long list of companies with current and historic links to the violence-ridden country.
Myanmar has been in turmoil since its military seized control in February this year, ousting the elected government. Security forces have killed at least 700 protesters and detained more than 3000 people.
According to the latest figures from December last year just under $100 million has been invested in those companies.
The fund has a decade-long shareholding in one of them, the Aviation Industry Corporation of China or AVIC, which sold more than $US500 million ($NZ686m) worth of combat aircraft to the military in 2018 and is also believed to have sold it missiles.
Green Party MP Golriz Ghahraman said it needs to stop.
"We're not talking about sort of civilian investment here and there, where you might be doing some roading work for a country that then has military coup. We're talking about actual military equipment, military aid in a force that we've know for decades to be committing atrocities in Myanmar."
Fourteen of the 24 companies have commercial ties to state agencies in Myanmar, now under military control. Other companies lease land from the junta for hotels and real estate development.
One of the most notable is KDDI, which helps operate MPT - a state-run mobile network. The Super Fund has almost $24m invested in it.
The military has largely controlled the network since the coup and has restricted access to the internet.
The Super Fund needs to be more transparent, Ghahraman said.
"Our Super Fund is answerable to the people of New Zealand and in fact they are governed by law that says that they're not supposed to invest where our international obligations have been undermined. That means they may have been acting unlawfully."
Consultants probing links to military - Super Fund
The fund hasn't yet itself confirmed what relationships the 24 companies have with the Myanmar military and junta. That is because it uses external consultants to research a company once allegations have been made about it.
A spokesperson for the fund said those consultants have been looking more closely into any links with Myanmar since February's coup.
"We don't reflexively exclude companies when issues emerge. We use international experts to monitor the business practices of the more than 6000 companies in the portfolio and our preference is to engage with individual companies where concerns arise.
"We are applying our framework with regard to companies that have been linked to Myanmar and the information supplied will form part of our investigative process.
"When focusing on a specific company, we consider the proximity and importance of the company's actions to the illegal or unethical activity.
"Where breaches are directly caused by the company, the course of action is much clearer than where the breach of human rights, environmental standards or corrupt practice is committed by a customer, supplier or even a state.
"With trade sanctions being relatively rare, companies can find it a challenge to avoid becoming linked to these activities if they are operating in, supplying to or buying from that country or state."
Finance Minister Grant Robertson was not available for an interview. But he said in a statement he has previously asked for assurances about the process the Super Fund operates for assessing whether the investments meet the "responsible" requirements and has been told Myanmar-linked shareholdings will be assessed under that criteria.
