Women dyeing their hair for the purpose of beautification

The basic principle concerning things other than acts of
worship is that they are permissible. Based on this it is permissible for a
woman to dye her hair if she wishes, unless it is black dye that is used to
conceal grey hairs, which is not permitted because the Prophet (peace
and blessings of Allaah be upon him) enjoined changing grey hair but he said
“avoid black”; or if this dye is something that is used only by kaafir women
such that if this woman was seen, people would say that she is a kaafir
woman, because no one uses this dye except kaafir women. In that case, it is
haraam for a woman to dye her hair with it, because the Prophet (peace
and blessings of Allaah be upon him) said: “Whoever imitates a people is one
of them.” If the dye is free from these two elements, i.e., black to cover
grey hairs and dye that is used only by kaafir women, then the basic
principle is that it is permissible, so the woman may dye her hair if she
wishes. End quote. 

Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him).