Praise be to Allah.
It is not permitted for a woman to shave her head except in cases of necessity, because of the hadith narrated by al-Tirmidhi and al-Nisaa’i from ‘Ali (may Allah be pleased with him) according to which the Prophet (peace and blessings of Allah be upon him) forbade women to shave their heads. Al-Khallaal reported from Qutaadah from ‘Ikrimah who said: “The Prophet (peace and blessings of Allah be upon him) forbade women to shave their heads.” Al-Hasan said: “This is mutilation.” Al-Athram said: “I heard Abu ‘Abd-Allah asking about a woman who was unable to take care of her hair properly and whether she should remove her hair according to the hadith of Maymoonah. He asked, ‘Why does she want to remove it?’ He said, ‘She cannot put oil on it or anything else that will make it look better, and she has a bad infestation of lice.’ He said, ‘If it is the matter of necessity, I hope that there is nothing wrong with doing so.’”
And Allah knows best.