An Iraqi-born refugee burnt the Muslim holy book outside a mosque on the first day of Eid al-Adha.
Swedish police charged him with agitation against an ethnic or national group last week.
Iran’s foreign minister, Hossein Amirabdollahian, blamed the government for granting him the protest permit.
Plans to burn copies of the Quran have sparked riots in Sweden in recent months.
Police had rejected similar protest applications recently, but courts then ruled that they should be allowed on freedom of expression grounds.
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