Some people claim that compulsory wearing of hijab is solely the interpretation of the Koran readers and religious interpreters or mullahs. However, it is very clear to any Quran reader that Hijab is compulsory.

Quran says (meaning English translation):
“And say to the believing women that they cast down their looks and guard their private parts and do not display their ornaments except what appears thereof, and let them wear their head-coverings over their bosoms, and not display their ornaments except to their husbands or their fathers, or the fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or their brothers’ sons, or their sisters’ sons, or their women, or those whom their right hands possess, or the male servants not having need (of women), or the children who have not attained knowledge of what is hidden of women; and let them not strike their feet so that what they hide of their ornaments may be known; and turn to Allah all of you, O believers! so that you may be successful. (31)”

“وَقُل لِّلْمُؤْمِنَاتِ يَغْضُضْنَ مِنْ أَبْصَارِهِنَّ وَيَحْفَظْنَ فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا ۖ وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ ۖ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ آبَائِهِنَّ أَوْ آبَاءِ بُعُولَتِهِنَّ أَوْ أَبْنَائِهِنَّ أَوْ أَبْنَاءِ بُعُولَتِهِنَّ أَوْ إِخْوَانِهِنَّ أَوْ بَنِي إِخْوَانِهِنَّ أَوْ بَنِي أَخَوَاتِهِنَّ أَوْ نِسَائِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَانُهُنَّ أَوِ التَّابِعِينَ غَيْرِ أُولِي الْإِرْبَةِ مِنَ الرِّجَالِ أَوِ الطِّفْلِ الَّذِينَ لَمْ يَظْهَرُوا عَلَىٰ عَوْرَاتِ النِّسَاءِ ۖ وَلَا يَضْرِبْنَ بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ ۚ وَتُوبُوا إِلَى اللَّهِ جَمِيعًا أَيُّهَ الْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ ﴿٣١
[Quran, chapter 24, verse 31]

You may refer also to the related question below for more information.

Rules regarding Muslim women’s (and men’s) attire are derived from the Quran, Islam’s revealed text, and the traditions (hadith) of the Prophet Muhammad (peace be upon him). In the Quran, God states: “Say to the believing men that they should lower their gaze and guard their modesty…And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and adornments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers…(a list of exceptions)” [Chapter 24, verses 30-31] Also, “O Prophet! Tell thy wives and daughters, and the believing women, that they should cast their outer garments over their persons…that they should be known and not molested.” [Chapter 33, verse 59] In general, girls are required to wear hijab at puberty, and throughout the rest of their lives, whenever they are in the company of males who are not their mahrems. A mahrem is a male so closely related that the girl/woman could never marry him.