Is Hijab Compulsory in Islam?
Question

Is hijab compulsory or something extra? If it is obligatory, is it obligatory for attractive and beautiful women only or for all Muslim women?
Praise be to Allah.Is hijab compulsory in Islam?
Hijab is obligatory for all Muslim women who have reached the age of puberty. In the answer to question no. 12525 you will find an explanation that the face is ‘awrah. We have already quoted the evidence that it is obligatory to cover it in the answer to question no. 21134  and 21536 . In the answer to question no. 11774  you will find detailed evidence stating that hijab is obligatory for all women. This general obligation is indicated by the verse in which Allah says (interpretation of the meaning): 
“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allah is Ever Oft-Forgiving, Most Merciful.” [al-Ahzab 33:59]
The women of the Muhajirin and Ansar obeyed that command. 
‘Aishah (may Allah be pleased with her) said: “May Allah have mercy on the first Muhajir women. When Allah revealed the words ‘and to draw their veils all over Juyubihinna (i.e. their bodies, faces, necks and bosoms)’ [al-Nur 24:31] they tore their aprons and covered their faces (ikhtamarna) with them.” (Narrated by al-Bukhari, 4480; Abu Dawud, 4102)
What is meant by ikhtamarna is covering the face, as al-Hafiz Ibn Hajar stated in al-Fath, 8/490. 
It was narrated that Umm Salamah said: When the words ‘draw their cloaks (veils) all over their bodies’ were revealed, the women of the Ansar went out as if there were crows on their heads because of the way they covered themselves. (Narrated by Abu Dawud, 4101; classed as sahih by Shaykh al-Albani in Sahih Abu Dawud)
Is hijab for beautiful women only?
Undoubtedly many of the women of the Muhajirin and Ansar were known to be blessed with beauty, but no one thought that this ruling applied only to them and not to others. 
These ahadith show that the women of the Muhajirin and Ansar obeyed the command to cover their faces and they did not understand the command as applying only to those who were beautiful.  
The scholars have explained that this ruling is general in meaning and applies to all women. 
In his commentary on the verse ‘draw their cloaks (veils) all over their bodies’, al-Jassas al-Hanafi (may Allah have mercy on him) said: 
“This verse indicates that young women are commanded to cover their faces in front of strangers (non-mahram men) and to be modest when they go out lest people with suspicious minds raise their hopes when they see them.” (Ahkam al-Quran, 5/245)
Ibn Jazi al-Kalbi al-Maliki (may Allah have mercy on him) said: 
“The Arab women used to uncover their faces as slave women do, which was an invitation to men to look at them. So Allah commanded them to cover themselves with their jilbabs and cover their faces with them.” (Al-Tas-hil li ‘Uloom al-Tanzil, 3/144) 
Shaykh al-Islam ibn Taymiyah (may Allah have mercy on him) said: “It is not permissible for women to uncover their faces where non-mahrams can see them. The people in authority have to enjoin what is good and forbid this evil and others. Whoever does not obey should be punished for that in a way that will deter him (from doing it again).” (Majmu’ al-Fatawa, 24/382)
Al-Suyuti (may Allah have mercy on him) said: 
“This is the verse of hijab which applies to all women and shows that they are obliged to cover their heads and faces.” (‘Awn al-Ma'bud, 11/106)
See also the answer to question no. 13646  
And Allah knows best.