Green Party co-leader James Shaw said the party wanted New Zealand to withhold support for Australia's bid for a seat on the United Nations' Human Rights Council, in protest against the country's human rights abuses.
The letter will be presented to Senator Lee Rhiannon from the Australian Green Party, who will table it in Parliament.
The Australian Greens have been outspoken in its criticism of the new immigration policy introduced last December and backed by the Australian Labor Party.
The change has seen non-Australians with a cumulative sentence of a year or more liable to be detained and eventually deported, with up to 1000 people to be sent to New Zealand.
Prime Minister John Key has been critical of the policy and unsuccessfully lobbied Mr Turnbull to reduce the threshold at which New Zealand citizens - many of whom have lived in Australia since infancy - would be deported.
Mr Turnbull has said more resources would be made available to clear a back-log of cases, and that any detainees could return to New Zealand while their appeals were heard.
Mrs Fox is in Sydney to meet with the family of some detainees.
Labour's Corrections spokesman Kelvin Davis is recently back in New Zealand after spending a week on Christmas Island, eventually being allowed in to the detention centre to meet eight detainees.
He said they were angry, hungry, and desperate, and he could not see any reason why they could not be allowed out in the community, under bail conditions, while their visa appeals were heard.
"If their visas are denied, I've got no problem. It is more the fact they are being detained when they could be home with their families - it is just a pointless exercise, that is really just a stupid political stunt to look like they are being hard on criminals."
Mr Davis said he had already written to Mr Turnbull in protest, and was surprised that officials from New Zealand's Ministry of Trade and Foreign Affairs (Mfat) had not visited detainees to check on their welfare.
Labour also expected New Zealand to withhold support for Australia's UN Human Rights Council bid because of the detentions, he said.