The Ministry of Health says there are two positive Covid-19 cases in Christchurch from the same household.

Covid-19 Response Minister Chris Hipkins says the case has been in Christchurch for up to a week.

One member of the household had recently returned to Christchurch from Auckland.

The case tested negative for Covid-19 before travelling to Christchurch, and got a second test once they became symptomatic, Hipkins said.

Hipkins said he cannot rule out a snap lockdown in Christchurch, but they are still waiting on more information before making that call.

The ministry says the local public health unit is identifying close contacts and exposure events, including any locations of interest.

A public health risk assessment is being done this morning and there will be an update after that.

Epidemiologist Michael Baker told Morning Report there's some inevitability about the coronavirus spreading through the country, but the South Island cases are still a shock.

He says New Zealand has a good contact tracing system so if it's just one case and a household contact it should be "manageable", and there may not be a need for alert level change. However the public health risk assessement will be helping determine that, he says.

"I think the wider question is how many other cases are incubating in the South Island."