It goes without saying that that the covering of a Muslim woman’s hair (or hijab) — an integral part of the Muslim woman’s dress code — is one of the prerequisites for the validity of the Prayer; therefore, performing Prayer without covering the woman’s hair is not acceptable.

Wael  Shihab, a Shari`ah researcher at Al-Azhar University, says: Before dealing with the issue of Prayer without hijab, or head-covering, we must remember that hijab is a well-established duty upon all Muslim women. This obligation is clearly stated in the Qur’an and the Prophet’s Sunnah. Therefore, as a Muslim woman, it is your right and your duty to wear hijab at every place: work, shops, etc. You should not obey your manager at the expense of disobeying God. Seek your right to wear hijab through all legal and peaceful channels, and never accept any compromise in this regard.
As for Prayer without hijab, covering the `awrah (parts of the body that should not be exposed in front of others) is one of the prerequisites of the validity of Prayer. For women `awrah is the entire body with the exception of the face and hands. Therefore, a Muslim woman’s Prayer cannot be accepted if she does not cover her `awrah.