The flight was scheduled to depart Auckland Airport at 9.05am March 3.
"Cabinet agreed to reinstate the temporary closure of the Cook Islands air border for a period of 72 hours effective midnight tonight."
The nation's cabinet will meet again on Monday to review the situation and will confirm whether or not to allow passengers on Friday's flight, it said.
"Cabinet made its decision based on up to the minute advice it received, which included information from the NZ Ministry of Health," Prime Minister Mark Brown said in the statement.
He also shared his appreciation for New Zealand Prime Minister Ardern and her officials for the "heads up" just prior to the late-night press conference in the Beehive last night.
"I also want to thank our local community for adhering to the advice of Te Marae Ora and Cook Islands Police and doing their part to keep our communities safe," Brown said.
Immigration Cook Islands will contact affected travellers directly and in the interim passengers are encouraged to change their flight arrangements.