The 37-year-old, who is retiring from all forms of international cricket after the T20 World Cup in June, did not feature in Friday's 72-run victory over the Black Caps as the Australians completed back-to-back wins over their hosts.
"Warner will require a brief recovery period, which is not expected to affect his availability for the upcoming Indian Premier League leading into the ICC Men's T20 World Cup," Cricket Australia said in a statement.
Warner hit 32 runs off 20 balls in the opening win over New Zealand in Wellington on Wednesday, but was booed off the field by the home fans in what was his final appearance in the bilateral international series.