Napier Port has decided the ship Ken Rei should remain offshore for a 14-day isolation period.
A port worker who tested positive for Covid-19 worked on the Ken Rei and one other ship in the past fortnight.
A letter of advice from the Ministry of Health claims the vessel can safely berth at any New Zealand port while following Covid 19 guidelines.
But Napier Port says the best precaution for its community is to keep the Ken Rei anchored offshore until Wednesday 28.
They say at that time, they will assess the circumstances of the vessel.
The Maritime Union of New Zealand said Monday the new Covid case showed there was an "urgent need" for coastal shipping reform.
Union national secretary Joe Fleetwood said the union had repeatedly raised concerns about the risk of having international ships carry domestic freight.
He said nearly all domestic sea freight was carried by international ships running international crews who were not covered by New Zealand law - meaning "every single one" of NZ's ports is an international border point and "it puts our members and the public at risk".
"Other nations run a small number of international ports as hubs for their protected domestic sea freight which give them greater control of their border security and of their supply chains.
"There's a reason our international airports are limited to large sites that can resource strong border security, we should be doing the same with our ports."
He said there should be two in the North Island and two in the South Island, which would be "secure and safe points of entry for goods.
"All other cargo should be shifted by New Zealand-flagged vessels that operate under our law and are staffed by people from our team of five million."
Fleetwood said the union had been talking to the Government "for a while" about the issue and both Labour and the Greens have "repeatedly backed the need to strengthen New Zealand-flagged coastal shipping".