Other posts expected to be closed include Madrid and the Hague, while posts in Warsaw, Vienna and Rome will be downsized and some of the property at the Paris Embassy will be sold.
Mr McCully defended the decision to close the Stockholm Embassy, which was set up by Labour only four years ago.
He said the relationship with Sweden was excellent "but in today's world it is not always necessary to have a diplomatic presence to maintain such a relationship".
Mr Goff said Mr McCully appeared to have a change of heart, given that 11 months ago, he had said that post should be kept.
"Asia is important, but it's also really important that we don't have all our eggs in one basket," Mr Goff said.
"We've learned that from past history and we need to make sure we are maintaining and extending our access in all important markets - not just one of them."
Mr McCully said the changes reflected the need to change to meet "current and future foreign policy and trade priorities".
He released part of a Mfat paper presented to the Cabinet which warned that changing overseas representation "must not be at the expense of key traditional relationships in Europe".
However, although the most growth was expected to happen in Asia with its growing middle class, New Zealand's foreign representation "reflects the balance of New Zealand's interests last century".
About 26 per cent of Mfat's expenditure was in Europe ($63.9 million) and although spending on Asia was higher than that ($75.1 million), only 7 per cent was in the Middle East and Africa ($18.8 million), which accounted for 40 per cent of the countries in the world.