Demonstrations have raged across Iran and Iraq after Denmark and Sweden allowed the burning of the Koran under rules protecting free speech. Protesters in Iraq set the Swedish embassy in Baghdad alight on Thursday.
Two anti-Islam protesters set fire to a copy of Islam's holy book in front of the Iraqi embassy in the Danish capital on Monday.
Iraq's foreign ministry called on authorities of EU countries to "quickly reconsider so-called freedom of expression and the right to demonstrate".
Protesters gathered in Baghdad on Saturday amid heavy security, with bridges leading to the Green Zone that houses many foreign embassies shut after an attempt by demonstrators to get to the Danish Embassy.
An Iraqi foreign ministry spokesperson said Danish staff at the embassy had left Iraq two days ago.
He did not elaborate on the reason or the exact timing and the Danish government did not immediately comment.
