The band said in a statement that the outbreak had led to a challenging few weeks.
"We have been monitoring the situation daily with our management and promoter partners. The recent rulings on international travel, the need to self-isolate and to cancel events of over 500 people have unfortunately made postponement of our shows the best present outcome.
Phoebe Bridgers will join The National on tour later in the year. Photo / Supplied
"We have a responsibility to our dedicated audiences, to our amazing crew, to our families at home, and to ourselves to take precautions in the interest of health and safety.
"For these reasons, we are moving our New Zealand and Australian performances with Phoebe Bridgers into December. We look forward very much to seeing you all at the end of the year."
It comes after a string of cancellations facing Kiwi concert-goers. Wellington's Homegrown music festival has been postponed until later in the year.
American folk-punk band Violent Femmes' Wellington and Auckland shows have also been postponed, as has Grammy award-winning Canadian Singer Alanis Morisette's upcoming New Zealand concert.
