بسم الله الرحمن الرحيم
In the Name of Allah most Gracious most Merciful
Iraq is mentioned (or referred to) in the Quran in a few places, this post will list them in order of the time the events mentioned in the Ayat happened along with a link to the tafseer of the Ayah for further information on the meaning of it and the different views that scholars have on it.
Ibraheem and Loot (ابراهيم و لوط)
Iraq was the land in which Ibraheem (May Peace and blessings be upon him) was born, and the land in which he gave Da’wah to his people, and the land from which he and Loot (لوط) made hijra from to Biladu Shaam (بلاد الشام).
ونجيناه ولوطاً إلى الأرض التي باركنا فيها للعالمين
And We delivered him and Lot to the land which We had blessed for the worlds.
ِAlthough there is a small difference between scholars on the land to which Ibraheem and Loot (لوط) were saved too, some say Shaam others say Makkah. For further information see: IslamWeb – Tafseer Attabari (Arabic)
After Sulayman (سليمان عليه السلام)
After the death of Prophet Sulayman (Peace be upon him) the nation of Bani Isra’eel started to decline, and corruption started entering the practices of traders and businessmen. The Qur’an mentions that Bani Isra’eel were prophesied to rise up and be corrupt in the land twice, and then fall.
The first prophesy was fulfilled by the Persians, then later on the Romans. When the Persians came, they did their doings, they took a group as prisoners, and went to Babylon in Iraq (link). Practice of magic was also prevalent among the Jews at this time, taught by the Shayateen after Sulayman, so Allah sent two angels as a test for them, those that failed the test lost the hereafter.
وَاتَّبَعُوا مَا تَتْلُو الشَّيَاطِينُ عَلَىٰ مُلْكِ سُلَيْمَانَ ۖ وَمَا كَفَرَ سُلَيْمَانُ وَلَٰكِنَّ الشَّيَاطِينَ كَفَرُوا يُعَلِّمُونَ النَّاسَ السِّحْرَ وَمَا أُنزِلَ عَلَى الْمَلَكَيْنِ بِبَابِلَ هَارُوتَ وَمَارُوتَ ۚ وَمَا يُعَلِّمَانِ مِنْ أَحَدٍ حَتَّىٰ يَقُولَا إِنَّمَا نَحْنُ فِتْنَةٌ فَلَا تَكْفُرْ ۖ فَيَتَعَلَّمُونَ مِنْهُمَا مَا يُفَرِّقُونَ بِهِ بَيْنَ الْمَرْءِ وَزَوْجِهِ ۚ وَمَا هُم بِضَارِّينَ بِهِ مِنْ أَحَدٍ إِلَّا بِإِذْنِ اللَّهِ ۚ وَيَتَعَلَّمُونَ مَا يَضُرُّهُمْ وَلَا يَنفَعُهُمْ ۚ وَلَقَدْ عَلِمُوا لَمَنِ اشْتَرَاهُ مَا لَهُ فِي الْآخِرَةِ مِنْ خَلَاقٍ ۚ وَلَبِئْسَ مَا شَرَوْا بِهِ أَنفُسَهُمْ ۚ لَوْ كَانُوا يَعْلَمُونَ
And they followed [instead] what the devils had recited during the reign of Solomon. It was not Solomon who disbelieved, but the devils disbelieved, teaching people magic and that which was revealed to the two angels at Babylon, Harut and Marut. But the two angels do not teach anyone unless they say, “We are a trial, so do not disbelieve [by practicing magic].” And [yet] they learn from them that by which they cause separation between a man and his wife. But they do not harm anyone through it except by permission of Allah . And the people learn what harms them and does not benefit them. But the Children of Israel certainly knew that whoever purchased the magic would not have in the Hereafter any share. And wretched is that for which they sold themselves, if they only knew.
The people of Yunus (Peace be upon him)
The people of Yunus, are those of the village of Ninawa in Iraq. They are a mix of the Assyrians and Jews under the kings of Babylon. When Yunus was sent to them he called them, and they did not listen, so Yunus became frustrated and left promising them the punishment of Allah. Before the punishment was upon them the people repented and believed and so the punishment did not befall them. (Link)
فَلَوْلَا كَانَتْ قَرْيَةٌ آمَنَتْ فَنَفَعَهَا إِيمَانُهَا إِلَّا قَوْمَ يُونُسَ لَمَّا آمَنُوا كَشَفْنَا عَنْهُمْ عَذَابَ الْخِزْيِ فِي الْحَيَاةِ الدُّنْيَا وَمَتَّعْنَاهُمْ إِلَىٰ حِينٍThen has there not been a [single] city that believed so its faith benefited it except the people of Jonah? When they believed, We removed from them the punishment of disgrace in worldly life andgave them enjoyment for a time.
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سبحان رب العزة عما يصفون، و سلام على المرسلين و الحمد لله رب العالمين