Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Using skin lightening cream as a beautification method is fine to use since it does not try to actually alter or mutilate your body the way tattoos or cosmetic surgery does.
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
Not being content with the color of your skin is often a psychological illness and usually a sign of having an inferiority complex. Prophet Muhammad (peace be upon him) taught that no white person has superiority over a black, nor the other way around.
People are influenced by their beauty industry to prefer certain body shapes and colors. No one is immune from the influence of the culture they are exposed to, but it is important to try to limit, and reverse, the effects on yourself as much as possible.
Using skin lightening cream as a beautification method is fine to use since it does not try to actually alter or mutilate your body the way tattoos or cosmetic surgery does. However, if this cream is used to deceive other people about the true color of your skin, such as a potential spouse, then it is unlawful.
Also, if the cream is harmful for your body, then it would also be disliked or prohibited depending on the amount of harm caused.
Abdullah ibn Mas`ud said: “Allah’s curse is on those women who make or get tattoos…and those who make space between their teeth artificially to beautify themselves. They are such that they change the nature and features created by Allah. Allah’s Messenger also cursed such women.” (Al-Bukhari and Muslim)
Almighty Allah knows best.
Source: Ask the Scholars