Sport itself is permissible, and may be desirable at times or obligatory. The Qur’an and the sunnah have urged all Muslims to attain strength, and sports are a means to staying strong. The sunnah encourages some useful sports, such as shooting, running, hand combats and training in war machines.
Boxing is one of the mediums of strength, but it is not permissible to professionalize it. It is just permissible to learn and train it, provided that training is not on humans, because of its dangers and harms, and because of the explicit prevention of the hitting of the face which is the mainstay of this sport.
According to the opinions of the European Council for Research and Fatwas: The Council affirms the rule that “professionalism is permissible” except for what was excluded by its evidence. Sports is allowed at the very least, if not obligatory, and the Messenger of God (peace be upon him) urged Muslims to adopt some types of sports that preserve the health of man and the strength of the ummah and as long as it does not lead to harm.
As for Boxing, it can be taken as a hobby, in a case wherein it is not by beating a human being, but by training on non-living bodies, this is permissible and not prohibited. Taking boxing as a profession is prohibited because of the damage done to the injured, it may have been a cause of death or permanent diagnosis, which is not permitted by the law of Islam, even if it was upon non-Muslims, as in the reality of the use of this sport, and the legitimate rule of Shariah is (do not cause harm nor retaliate).
Boxing also involves hitting at the head and face, and the Prophet has said, “If any of you fights (in a narration: if he hits) the other, let him avoid the face.”