OTTAWA—Canada said Friday it had shut its embassy in Tehran and would expel all Iranian diplomats in the country, severing diplomatic ties amid a stepped-up campaign by the U.S. and its allies to isolate Iran over its nuclear ambitions.

Canadian Foreign Affairs Minister John Baird said in a statement Friday that Canada has closed its embassy in Iran, effective immediately, and ordered the expulsion of all Iranian diplomats in the country, arguing Tehran represents the biggest threat to global security.

The...