The scholars (sunni) has unanimously agreed that boxing as practiced nowadays in contests and sport centers in our countries is a prohibited practice in the Islamic Shari`ah. It is based on permitting fighters to injure each other to the extent that could lead to blindness, permanent severe brain damage, serious fractures, or death; without imposing any liability on the other party. In addition, spectators derive pleasure from the winner's victory and feelings of happiness for the injury suffered by the loser. This is absolutely prohibited and rejected in Islam for Allah states (Exalted be He) :
...and do not throw yourselves into destruction [Surah Al-Baqarah 2:195]
And His Statement (Exalted be He):
And do not kill yourselves (nor kill one another). Surely, Allâh is
Most Merciful to you. [Surah Al-Nisa 4:29]
In addition to the statement of the Prophet (peace be upon him):
There should be neither causing nor reciprocating harm. [Sunan Ibn Majah no. 2340]
Second: Freestyle Wrestling:
As for freestyle wrestling in which wrestlers deem it lawful to hurt one another and cause injury, the council views that it completely resembles boxing even if there are slight differences between them, because the legal physical reasons for the prohibitions of boxing exist in freestyle wrestling that assumes the nature of fighting. Thus, it takes the same ruling of prohibition. Regarding other types of wrestling practiced for physical exercise without causing any injury, they are legally permissible and the council does not view their prohibition.
The other opinion is :
There is no harm in practicing freestyle wrestling so long as it does not involve danger, harm, or uncovering one's Awrah (parts of the body that must be covered in public). The Hadith mentions that:
Prophet (peace be upon him) wrestled Yazid ibn Rukanah and defeated
him (peace be upon him). [Sunan Abu Dawud no.4078]
This is because the basic ruling expresses permission unless otherwise declared by Islamic law.
So as long as there is no harm to anyone involved or uncovering one's Awrah, it is permissible to practice this type of wrestling.
Moreover, it is permissible to practice arts of fighting for the cause of Jihad.
And make ready against them all you can of power, including steeds of
war (tanks, planes, missiles, artillery) to threaten the enemy of
Allâh and your enemy [Surah Al-Anfal, 8: 60]
And there are martial arts which require bowing to the opponent and such an act of bowing is not permissible since bowing is a religious act of Ibadah (worship) and Ibadah should be devoted to Allah Alone.
Source: The ruling on boxing, bullfighting, and freestyle wrestling
What are the categories of permissible games in Islam?
Martial arts with bowing