Two of these six results have been deemed "historical"; four have been confirmed as new.
As a consequence, the Pakistan team's exemption to train while in managed isolation has been put on hold until investigations have been completed, NZC said.
Separately, NZC has also been made aware that some members of the Pakistan team had contravened protocols on the first day of managed isolation.
"We will be having discussions with the tourists to assist them in understanding the requirements," the statement said.
Pakistan are set to face the Black Caps in three T20 internationals and two tests, with the first match on 18 December.
The Ministry of Health revealed that several team members have been seen on CCTV at the facility breaching managed isolation rules, despite "clear, consistent and detailed communication of expected behaviours while in the facility."
In a statement, the Ministry said that the team as a whole has been issued with a final warning.
All members of the team returned a negative Covid-19 test and passed a symptom check before departing Lahore.
Fifty-three members of the squad arrived in Christchurch on 24 November and were tested on day one, with the six cases coming as a result of the tests.
All cases are being moved to quarantine rooms within the facility at the Chateau on the Park hotel. Members of the team will be tested a minimum of four times while in managed isolation.
The Medical Officer of Health at Canterbury District Health Board has sent a letter to the squad's management to be communicated to the whole team, reinforcing that all team members are required to stay in their rooms until advised otherwise.
Director-General of Health Dr Ashley Bloomfield said any breaches of managed isolation rules were taken very seriously.
"It is a privilege to come to New Zealand to play sport, but in return teams must stick to the rules that are designed to keep Covid-19 out of our communities and keep our staff safe."
Air Commodore Darryn Webb, head of Managed Isolation and Quarantine, said there are robust processes in place in managed isolation facilities to respond to these events.
"Our focus is on keeping the rest of the squad and our staff safe. For that reason, all other team members must remain in their rooms while investigations continue. This is in line with standard operating procedures at managed isolation facilities."
--More to come
