He said it made sense for "first cousins" like Britain and other Commonwealth countries to share embassies.
"As [British Prime Minister] David Cameron said when addressing the Canadian parliament last year, 'We are two nations, but under one Queen and united by one set of values'," Mr Hague said in a statement.
"We have stood shoulder to shoulder from the great wars of the last century to fighting terrorists in Afghanistan and supporting Arab Spring nations like Libya and Syria.
"We are first cousins.
"So it is natural that we look to link up our embassies with Canada's in places where that suits both countries. It will give us a bigger reach abroad for our businesses and people for less cost."
A British diplomat told the Daily Mail the move by Hague, a known Euro-sceptic, could be seen as an attempt to counter the influence of Brussels.
"For all the grandiose talk of European unity, we have so much more in common with many Commonwealth countries than the EU - and not just the English language," the source said.
"There is a saying in the British diplomatic corps that 'the French want to do us over, the Germans want to lord it over us and the Italians are all over the place'.
"We would never dream of trusting them with intelligence secrets, but we share everything with the Canadians, Aussies and Kiwis.
"Brussels can extend its diplomatic reach - well, so can we."
New Zealand's Minister of Foreign Affairs Murray McCully indicated the shared diplomatic missions were a possibility.
"We already co-locate with the UK in Kabul and have had positive discussions about co-location elsewhere."
