from Darul Uloom Abu Bakr, of Port Elizabeth, South Africa
Q: Can a person read Quran without a cap? What is the ruling 4 men and women?
A: The Ulema have mentioned that among the aadaab or ettiquette of Quran recitation one is to cover the head. So though it is permissible to read Quran with the head open, it is makrooh (disapproved) because this is contrary to respect.
For a woman it is not permissible to recite Quran with the head and hair uncovered. This law will be stricter in the case of woman, as is the case in salah. A man's salaah is makrooh but valid if he does not wear a cap (topi). However, the woman's salaah is not valid at all if she performs salaah without head and hair covered. The same principle will apply to Quran reading.