The far-right group on Monday posted a video in which a man is seen desecrating and burning what appeared to be the Muslim holy book, and trampling an Iraqi flag.
The latest video following a similar event on Friday and others in recent weeks in Sweden's capital.
Iraq's foreign ministry “strongly condemns, again, the repetition of the burning of a copy of the holy Quran in front of the Iraqi embassy in Denmark,” it said in a statement.
Such acts allow “the virus of extremism and hate” to pose “a real threat to the peaceful coexistence of societies”, the ministry added.
Ministry spokesman Ahmed al-Sahhaf meanwhile said the Danish embassy's diplomatic staff already left Iraq on Saturday.
Nearly a thousand protesters had gathered in Baghdad on Saturday at the call of Iraqi Shia cleric Muqtada al-Sadr, following the first incident in Copenhagen.
They attempted to march to the Danish embassy in Baghdad's fortified Green Zone but security forces blocking two bridges to the area repelled them with tear gas and batons.
Sadr's supporters had on Thursday set alight the Swedish embassy in Baghdad following two similar events in which a Stockholm-based Iraqi refugee desecrated the Quran.
Iraqi authorities condemned the burning of the embassy, while retaliating against Stockholm for permitting protests in which the Quran was desecrated by announcing the expulsion of the Swedish ambassador.
Swedish authorities had allowed the demonstrations on free-speech grounds but said their permission did not signal any approval of the action.
Iraqi Prime Minister Mohamed Shia al-Sudani on Monday met with ambassadors from other European Union countries, during which he again slammed the desecrations.
He said the actions “have nothing to do with freedom of expression” and called on EU countries to “fight such racist acts and all those that incite violence”, according to a statement.