Can women learn martial arts for their protection, if it involves fighting with men?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If there is a facility where women can learn martial arts for the purpose given without mixing with the opposite sex or uncovering their Awrah (the parts of the body which must be covered) or neglecting their obligations, then it is not prohibited in Shari'a. We advise our sisters however to protect their dignity and keep from wasting their time in such activities.
Know that safety and protection of a woman lies only in adhering to the rulings of Shari'a and taking the good women ancestors as their ideal. The most distinguishing quality of those women was staying at home and not leaving except for necessity, following the Command of Allah. {And stay in your houses, …} [33:33].
Allah knows best.