Genter said the issue was particularly acute for those placed in default KiwiSaver schemes who had wound up exposed to the controversial industries.
"You would expect they'd be required to comply with the law before being allowed to sign people up," she said.
A Herald investigation into the sector found more than 1.8 million New Zealanders had invested in funds which had invested at least $43 million to companies producing such weapons.
The advice - weighing up The Cluster Munitions Prohibition Act, The Nuclear Free Zone, Disarmament and Arms Control Act and The Anti-Personnel Mines Prohibition Act - concluded "The Police are responsible for investigations in respect of these laws".
A Police spokesperson this afternoon said they were aware of the issue and had begun asking questions.
"Police are making enquiries with other agencies to gather more information. This will be assessed as appropriate in due course," the spokesperson said.
Goldsmith said he and his officials had not formally referred the matter to Police, but it was not his place to request they pick up the issue.
"It's not appropriate as a Minister for me to suggest what the Police should be doing. It's up to them, like any enforcement agency, to weigh up all the factors."
He agreed the ball was now in Police's court: "Well, yeah: They're the appropriate authority."
Goldsmith sought the advice following a Herald investigation into KiwiSaver holdings, and an independent series of stories from RNZ, that showed KiwiSaver investors had invested millions into companies producing weapons banned by New Zealand and international law.
The Dirty Secrets of KiwiSaver analysis found $4.3m of client funds had been invested into landmine producers, $2.3m into cluster-bomb makers and $36.9m into nuclear weapon-producers.
In response a number of KiwiSaver providers found to have invested in cluster bomb producers - including Westpac and Aon - announced internal reviews. Grosnover and AMP went further and announced they would take immediate steps to divest their holdings.