A more full review would also include three other recent incidents involving the vessels Playa Zahara, the Viking Bay and the Mattina - all of which had Covid crew cases aboard.
"Managing public health risk remains our top priority. However, officials must also consider the potential impact of any New Zealand-specific health-based restrictions on international trade," said the ministry.
"New Zealand, like many other countries, is already experiencing economic disruption from international cargo shipping delays. New Zealand's protections are in line with international requirements, and any further restrictions would need to continue to carefully balance these various factors."
No date had been set for a final report on the incidents. The ministry would work with other government agencies involved to ensure the review considered all aspects, not just public health, the statement said.
Eleven crew members on the Rio de la Plata tested positive for the Delta variant of the virus, leading to an 11th-hour order for Tauranga port stevedores and others who had been in contact with the ship to self-isolate and undergo testing.
The port workers, the bulk of whom had not been vaccinated according to the Government, all tested negative and have been cleared to return to work at New Zealand's biggest port.
Port of Tauranga chief executive Leonard Sampson told the Herald the container ship had a flag on it, which meant not to bring it into port. But the port, shortly after the ship's arrival in Bay of Plenty waters, had received an advisory it was cleared to berth.
The initial alert about the vessel came from Maritime NZ to the port's marine operations manager.
The port said all ships also needed "a pratique clearance" from the local public health unit's medical officer of health. Customs had a role in permitting cargo loading and unloading, and in the Rio de la Plata case, the Ministry of Health was involved too.
The vessel departed the port last weekend with all its asymptomatic crew aboard.
The ministry statement said all ships coming to New Zealand from overseas are treated as if the ship has Covid-19 on board. Protocols were in place to manage these risks.
The ministry understood from Bay of Plenty public health staff that all infection prevention controls, and PPE protocol, were followed by Port of Tauranga workers who had contact with the Rio de la Plata container ship during their duties.
Public health staff had assessed that the risk posed to the Tauranga community by the vessel's Covid cases was low, and the steps taken to date are appropriately managing any risks.
"For this reason, there are currently no restrictions on events in Tauranga.
"As a precaution, the ministry is asking port workers, their close contacts and the Tauranga community to remain vigilant for Covid-19-like symptoms and follow all health advice."