The palace released a photo of them at William’s London residence.
A spokesman for the duke said the meeting took place on Saturday.
Ms Ardern was in London for talks with Prime Minister Boris Johnson, with trade and the war in Ukraine dominating the agenda.
Mr. Johnson greeted Ms Ardern on Friday with a handshake outside the door of Number 10 and welcomed her on her first British trip since the pandemic began.
Mr Johnson pointed out that this was her first trip since the two countries signed a new free trade agreement in February.