Can Women Read Quran Without Hijab?

It is not obligatory for a woman to put on hijab in order to read the Quran, because there is no evidence to indicate that this is obligatory. 

Shaykh Ibn ‘Uthaymin said that reciting the Quran does not require covering the head. 

Shaykh Ibn ‘Uthaymin said in his comments on sujud al-tilawah (prostration required when reading certain verses of the Quran): “Sujud al-tilawah is to be done when reading the Quran. It may be done in any state, even with the head uncovered , etc., because this prostration is not subject to the rulings on prayer.” (Fatawa al-Jami’ah li’l-mar-ah al-Muslimah, 1/249) 

“With regard to reading Quran, it is not permissible for one who is in a state of janabah (impurity following sexual activity) to read Quran either from the Mus-haf or otherwise until he has done ghusl, because it was narrated that nothing prevented the Prophet (peace and blessings of Allah be upon him) from reading Quran except janabah. But if a person has broken his wudu (minor impurity), then it is permissible for him to recite the Quran from memory because of the general meaning of the evidence.” (Majmu’ Fatawa al-Shaykh Ibn Baz, 10/150) 

It is better, and is mustahabb, to do wudu before reciting, because this Quran is the Word of Allah. So it is better to do wudu before reading it as a sign of respect. But touching the Mus-haf is not permissible unless one has done wudu, because Allah says (interpretation of the meaning): 

“Which (that Book with Allah) none can touch but the purified.” [Al-Waqi’ah 56:79] (Majmu’ Fatawa al-Shaykh Ibn Baz, 10/150) 

With regard to women who are menstruating or bleeding following childbirth, please see Question no. 2564 .

And Allah knows best.