Iraq's Foreign Ministry condemned "in strict terms" the second such protest in days outside its mission in Copenhagen.
It called on members of the EU to "quickly reconsider so-called freedom of expression and the right to demonstrate", state media said.
An organiser of Monday's protest trod on the Quran and set it alight in a tray next to an Iraqi flag, Reuters reported.
The two Copenhagen stunts on Friday and Monday were carried out by members of a far-right group called Danish Patriots.
They followed a series of similar episodes in Sweden that have strained the country's international relations.
Such acts allow "the virus of extremism and hate" to pose "a real threat to the peaceful coexistence of societies", the Iraqi ministry added.
Demonstrators in Baghdad stormed Sweden's embassy last week and blocked a bridge on Saturday in protest at events in Denmark.
Iraq on Monday said Danish diplomatic staff had left Baghdad, amid anger at the Nordic countries for condoning protests where the Quran was burnt.
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 Mohammed Shia Al Sudani on Monday met ambassadors from EU countries, during which he again condemned the desecrations.
He said the actions had "nothing to do with freedom of expression" and called on EU countries to "fight such racist acts and all those that incite violence".
Turkey strongly condemned the "despicable attack" and called on Denmark to take necessary measures to prevent this "hate crime" against Islam, its Foreign Ministry said.
A US National Security Council official told The National that President Joe Biden's administration "notes the value of diplomatic engagement to address challenging issues” as Baghdad considers its steps.
Washington also emphasised that it believes the Quran burnings are "offensive," while more generally supporting Sweden and Denmark's "strong protections for freedom of expression".
"It’s abhorrent for anyone to burn or deface a religious book that is held in honour by so many people around the world," the White House official told The National.
"Demonstrations such as the ones we have seen could create an environment of fear that impacts the ability of Muslims and members of other religious minority groups to freely exercising their right to freedom of religion or belief."
Germany's Defence Minister Boris Pistorius cancelled a trip to Iraq over security fears, while the 57-member Organisation of Islamic Co-operation suspended the status of a Swedish special envoy.
"The Council reiterates it unequivocally rejects such heinous acts that aim to provoke Muslims around the world, while also emphasising that the recurrence of such racist actions reflects a vile extremism, blind fanaticism and abhorrent hatred, that contradict basic human principles and norms," it said.
"Furthermore, these abhorrent acts only serve to undermine global efforts to promote peace and coexistence."