The person is currently in managed isolation, however, it is unclear whether or not they have come from overseas or have been in the community.
"There is one case currently under investigation in Canterbury," the Ministry said in a statement.
"This case is in managed isolation."
"At any one time, it is standard to have cases under investigation and as such, these aren't included in any numbers update at this stage."
Anyone who is feeling unwell should stay home and consult their GP or ring Healthline if they display Covid-19 like symptoms, the Ministry also said.
Twelve people have died from the virus in Christchurch, 10 of those at the Rosewood Rest Home, with the city recording 164 total cases of Covid-19.
It comes as two deaths relating to the virus were reported in as many days, both in Auckland.
The first was a man aged in his 50s, the youngest to die in New Zealand, and the second was Dr Joseph Williams, a former Cook Islands Prime Minister.
Dr Williams, 85, was a much-respected general practitioner in Auckland and died less than 24 hours after his older brother died from the virus.
The 85-year-old's nephew Dr Kiki Maoate said the double tragedy has hit the family hard: "It is a blow for the family. They are reeling from it," he said.
Dr Williams is the 24th person in New Zealand to die from Covid-19.
Earlier today it was revealed there are three new cases of Covid-19 in New Zealand, two of whom are in the community and the other in managed isolation.
Both community cases are epidemiologically linked to the wider Auckland cluster, the Ministry of Health said in a statement.
