SYDNEY—Having advertised its annual budget delivered Thursday as a “no frills” affair, the New Zealand government instead unveiled a generous increase in fiscal stimulus that could result in a harsh response by the country’s inflation-weary central bank as early as next week.

Increased funding to help meet a significant repair bill from a cyclone that battered the country’s north in February was the centerpiece of the budget for 2023-24, with the government saying it now expects the agriculture-rich economy to avoid a recession…