Cody was generating large easterly swells that were set to affect the eastern coast of the North Island from Saturday through to Tuesday, MetService said.
And the cyclone would bring with it a "tropical air mass" which meant heavy rain was likely in the northeast of the North Island on Monday, along with gale force winds.
"Hazardous conditions are expected about exposed eastern coastlines of the North Island, where large easterly swells, significant sea surges/rips and coastal inundation are possible."
Those conditions would be caused by gale and storm-force winds from offshore and as the cyclone approached the northeast of the island.
Northland is likely to see very big waves from Saturday and they are set to arrive in the Bay of Plenty and Coromandel on Sunday as the cyclone moves south, according to MetService meteorologist Angus Hines.
Gisborne and Hawkes Bay would then see "very, very heavy swell" before Monday brought big waves further south along the east coast - possibly down to Marlborough.
Gisborne Mayor Rehette Stotlz earlier told RNZ people needed to be careful and stay clear of beaches.
"Everyone that lives along the beach just watch out for what is going on there, and then again, as always, we might see some surface flooding."
Civil Defence teams had been checking in with communities and campers along the Gisborne coastline to make sure they were aware of the cyclone, while there was a high chance some beaches could be closed, RNZ reported.
Weatherwatch's Philip Duncan Cody would now technically become an ex-cyclone as it was no longer tropical - but it would still be a powerful storm.
The latest modelling showed Cody would track closest to New Zealand on Monday but water conditions would go downhill rapidly on Sunday as swells arrived.
"Very dangerous conditions - rips, currents and rogue waves - so unless you're very experienced we would recommend that pretty much everybody stays out of the water as this storm comes in closer," Duncan said.
He said it was possible Gisborne could see 120-150mm of rain brought by the weather system.
A heavy rain watch is in place from midnight on Sunday to midnight on Monday for Gisborne and the Wairoa District, MetService said.
Periods of heavy rain are forecast in the area and it's possible the amounts may reach warning criteria.
A strong wind watch is also in place over that time for Bay of Plenty east of Whakatane and Gisborne north of Tokomaru Bay.
The forecast is for south to southeast winds that could approach severe gale speed in exposed places.
Elsewhere it was possible Hawke's Bay, Gisborne and the far east of Bay of Plenty to see warning amounts of rainfall and severe gales on Monday and early Tuesday. There was also a lower risk of heavy rain and severe gales for Bay of Plenty, Taupo, eastern Taihape and Wairarapa.
MetService forecast the weather would remain fine until Cody arrived, and that fine weather would continue into next week for western and southern areas that were minimally affected by the cyclone.
