A Christchurch supermarket has been closed after it was visited by a person who later tested positive for Covid-19 in South Korea.

The Countdown at Spitfire Square, near Christchurch Airport, is undergoing a deeper clean than usual.

Countdown spokesperson Kiri Hannifin said the cleaning is a precaution.

She said the order was made after the company was contacted by the Canterbury District Health Board in relation to the person who tested positive in South Korea.

It's been more than a week since the person went through the store.

However, Kiri Hannifin said the stores are cleaned every day. She expects it to reopen tomorrow morning.

A Ministry of Health spokeswoman said that the supermarket store was closed for a deep clean Tuesday, as per their precautionary approach connected to the positive test of the person who travelled from New Zealand to Korea earlier this week.

"The Ministry of Health and local DHB did not require the closure of the store as the risk is low, but do appreciate the effort Countdown have gone to," she said.

The Countdown is a five-minute walk from the Sudima Hotel and is opposite a hair and beauty salon, a Coffee Club cafe and an Anytime Fitness gym in a shopping complex.

A Sudima Hotel spokeswoman confirmed it was being used as a managed isolation facility and directed further queries to the Government response team.

A hotel spokeswoman said she was unaware of the claims a guest might have wandered to the Countdown.

Earlier today, Health Minister Chris Hipkins said there was no evidence the person who tested positive for Covid-19 in South Korea after travelling from New Zealand was infected here.

But amid an "abundance of caution", officials were contact-tracing two rows in front of and behind the person, who left New Zealand from Christchurch Airport on July 21.

The person had been in New Zealand since March 18 on a visitor's visa.

On Monday, it was revealed that the man in his 20s had tested positive a day after taking a plane from Auckland to Christchurch before continuing overseas to South Korea last week.

Initially presenting as asymptomatic, Korean-language news services say the man is now in hospital under quarantine. Meanwhile, health authorities in both countries are trying to pinpoint where he caught the virus.

The Ministry of Health said they could not rule out the man became infected in New Zealand before travelling to South Korea.

He was admitted to Dongsan Hospital immediately for quarantine treatment.

The Health Ministry said the traveller left New Zealand a week ago on July 21 and arrived in South Korea on July 22 after transiting through Singapore.