All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Hijaab is an obligation ordained and prescribed by Allah The Almighty on women. Allah Says (what means): {O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.} [Quran 33: 59]
In another Soorah (chapter of the Quran), Allah Says (what means): {And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.} [Quran 24:31]
Therefore, it is imperative on the Muslim men and women to submit to the commands of Allah and those of His Prophet in accordance with the true faith (Iman). Allah Says (what means): {It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error.} [Quran 33:36]
If the woman does not fulfill the obligation of wearing Hijaab, then she is prone to the punishment and wrath of Allah.
However, there is no authority from the Quran or Sunnah (sayings of the Prophet ) indicating clearly the type of penalty. Even if it is but a minor penalty, nobody can endure the Hellfire for a moment. The Muslim woman should fear Allah The Almighty and fulfill her obligations towards her Lord. If a woman committed a sin, she should repent as quickly as possible before it is too late.
For more benefit on the evidence for Hijaab and its conditions, please refer to Fataawa 81554, 83765, 83702, 81494, 354259 and 83033.
Allah knows best.