The second person to test positive was in isolation at home in Christchurch but would be moved to a managed isolation facility. Meanwhile, the person to test positive on Monday remained in self isolation at their home.
The person was tested as part of the routine testing for staff at the hotel and returned a negative test on Thursday. They are asymptomatic and the virus was only picked up when they were retested as a close contact of Monday's positive case. They returned a positive test yesterday.
Two close contacts of the person have been identified - both household contacts who were to be tested and would self isolate at home.
"At this stage the Ministry is not advising of any need to change the current approach," the Ministry said. "Both cases have limited numbers of contacts and the incident is currently well contained."
Genome sequencing of Monday's case would be completed this evening, at the earliest, and will be revealed today.
The first group of international mariners quarantining at the Sudima, who were due to leave the facility yesterday after completing their isolation period, will now stay at the hotel for a further 48 hours as an additional precautionary measure, as hotel staff members were tested for the virus.
"Those precautionary measures have included additional tests – up to four tests for some individuals - and an already lengthened stay in managed isolation."
The Ministry of Health will reveal more information on the new case of Covid-19 today at 1pm.
A pop up Covid-19 testing centre will be set up in the carpark of the Princess Margaret Hospital car park for today only, the Canterbury District Health Board says.
Dr Hannah Gordon, a community based testing clinical leader, says it's an ideal testing site as it is close to Cashmere High School and the Countdown in Colombo Street.
"While we don't believe there is any risk for Cashmere High students, we understand that many people may be concerned and will be keen to get tested," she said.
"With regard to the Countdown in Colombo Street the risk to anyone who was in store between 11.30am and 12.30pm on Sunday 1 November is considered extremely low, however we will be here for anyone who wants to pop in and get tested. At present you don't need to have symptoms to qualify for free testing."
A total of 31 positive Covid cases have now been linked to a group of mariners who are among 440 fishers from Russia and the Ukraine.
Of the more than 400 to arrive in Christchurch, 270 were due to go out on three Independent Fisheries boats next month.
The international fishermen have exclusively stayed at the Sudima Christchurch Airport since their arrival in October.
Air Commodore Darryn Webb earlier told Chris Lynch on Newstalk ZB that international Covid hotspots such as Russia were higher risk for recent arrivals.
There was a 24-hour delay as the aircraft worked through its process in Moscow and the fishermen were assembled there for 48 hours and then en route for 18 hours - which provided an opportunity for the virus to spread, he said.
Where to get a test:
• The Princess Margaret Hospital, 95 Cashmere Rd. Open 11.30am until 4.30pm Wednesday.
• Orchard Road Community Based Assessment Centre: 174 Orchard Road, Christchurch. Open 9am-4pm, 7 days a week.
• Whānau Ora Community Clinic Community Based Assessment Centre: 250 Pages Road, Wainoni, Christchurch. Open 9am-4pm, 7 days a week.
• Most general practises in Canterbury offer free Covid-19 tests.