"The restrictions are changing regularly and we have now entered a period of uncertainty on how long these measures will be in place. Your safety, as well as the safety of artists and our staff is of utmost importance to us."
The statement says new dates will be worked out with the artists as soon as possible, and that tickets will remain valid for the new show.
"We are working tirelessly with The Offspring and Sum 41 to reschedule the tour and will bring you information on new dates as soon as we can."
The Offspring have sold more than 40 million albums worldwide, and their Australian and New Zealand tour was their first headline tour in 16 years.
The concert is one of several entertainment events to be postponed recently since the Government placed restrictions on public gatherings to help stop the spread of Covid-19.
American band The National have also postponed their Auckland shows, as has Grammy award-winning Canadian Singer Alanis Morisette's upcoming Spark Arena concert.