The Pakistan squad are now in managed isolation in Christchurch, where they arrived on Tuesday for a tour scheduled to include two Tests and three T20 matches.
"It is a privilege to come to New Zealand to play sport, but in return teams must stick to the rules that are created to keep Covid-19 out of our communities", director-general of health, Ashley Bloomfield, said in a statement.
Six members of the Pakistan touring cricket squad, now in managed isolation in Christchurch, have tested positive for Covid-19.
In a statement posted on its website, NZC said it was "made aware today that six members of the Pakistan touring squad, now in managed isolation in Christchurch, have tested positive for Covid-19".
The outcome was "disappointing for the Pakistan squad" but the "testing outcomes and the actions taken show the government system is working", NZC said.
Bloomfield said CCTV showed members of the tour party breaching social distancing protocols.
Prior to leaving Lahore, all members of the Pakistan squad returned negative results on the four occasions they were tested.
Director-General of Health Dr Ashley Bloomfield says visiting sports teams "must stick to the rules".
Meanwhile, the country's director general of health, Ashley Bloomfield, said in a statement: "It is a privilege to come to New Zealand to play sport, but in return teams must stick to the rules that are created to keep Covid-19 out of our communities".
New Zealand has been widely praised for its approach to handling the coronavirus and has reported just over 2,000 total cases and 25 deaths since the pandemic began, according to the John Hopkins University of Medicine.
New Zealand's Ministry of Health said the breaches of isolation rules occurred "despite clear, consistent and detailed communication of expected behaviours while in the facility".
"We will be having discussions with the tourists to assist them in understanding the requirements", the statement said.
After the series against West Indies, starting Friday (November 27), New Zealand are set to play three T20Is and two Tests against Pakistan, starting December 10.
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".
At least 10 Pakistan cricketers had tested positive for COVID-19 before the team's England tour earlier this year. The team has also been stopped from training until further investigation.