SYDNEY—New Zealand will move to the highest level of its Covid-19 restrictions as it seeks to contain an Omicron-variant outbreak that also led Prime Minister Jacinda Ardern to cancel her wedding plans.

Ms. Ardern said on Sunday that nine Covid-19 cases in the Nelson Marlborough region, on the country’s South Island, had been confirmed as Omicron. The nine cases are from a single family who flew earlier this month to Auckland—New Zealand’s largest city, located on the North Island—to attend a wedding and other events. A further case from the same household has also been confirmed.