There is a statement in the Quran:
"And those who guard their chastity, except in the case of their wives or those whom their right hands possess, - for then, they are free from blame; but whoever seeks beyond that, then those are transgressors." -23:5-7.(The Qur'an, chapter 23 (Al-Muminun), verse 5 to 7)
As the above ayah shows, masturbation is not allowed in Islam.
Many scholars are of the opinion that if it was allowed, it would have been explicitly mentioned in the above ayah. As it has not been mentioned, it is taken to be completely forbidden.
At least one Islamic legal tradition forbids masturbation on the authority of an Ayah of the Quran which indicates that those who seek sexual gratification from other than their legal sexual partners are transgressing set limits. This is interpreted to refer not only to adultery but to masturbation as well.
Some Hadith that are quoted to in support of masturbation being Haram (forbidden, not allowed) include:
A narration reports:We were with the Prophet (SAW) while we were young and had no wealth whatsoever. The Prophet (SAW) said: "O assembly of youths; whoever among you possesses the physical and financial resources to marry should do so, because it helps him guard his modesty, and whoever is unable to marry should fast, as fasting diminishes his sexual power."
Sahih Muslim and Sahih Bukhari includes
A narration attributed to Abd-Allah ibn Mas'ud reports:Rasulullah (Sallallaahu Álayhi Wasallam) said, 'O group of youth! Whoever from among you can marry should do so because it keeps the gaze low and it protects the private parts. And he who cannot marry should make it compulsory upon himself to fast because it breaks lust.'
Ibn Kathir has wrote in volume 5 p. 458
A narration attributed to Hasan ibn Arfah reports:Nabi (Sallallaahu Álayhi Wasallam) said, '7 (Seven) persons are such that Allah will not look at them on the Day of Qiyaamat nor will He purify them nor will He include them among the learned and Allah will enter them into Jahannam. They will enter Jahannam first except for those who repent. As those who repent Allah will accept their repentance.1) A person who masturbates.2) A person who performs the act of sodomy.3) The person upon whom the act of sodomy is performed.4) A perpetual drunkard.5) The person who hits his parents so much that they appeal for help.6) The person who harms his neighbors so much so that they curse him.7) The person who commits adultery with his neighbor's wife.
Other quoted material includes from Tafsir al-Mazhari vol. 12 p. 94
A narration attributed to Anas ibn Malik reports:Rasulullah (Sallallaahu Álayhi Wasallam) said, 'the person who performs Nikah with his hands (i.e. masturbates) is cursed.
Quoted from those after the Sahaba
A narration attributed to Sa'id ibn Jubayr reports:Rasulullah (Sallallaahu Álayhi Wasallam) said, 'Allah Taãla will inflict a punishment on a group of people because they played with their private parts.'
A narration attributed to Ata ibn Abi Rabah reports:Some people will be resurrected in such a condition that their hands will be pregnant; I think they are those who masturbate.
Scholars of Islam do not approve of masturbation, except in extenuating circumstances. Some scholars state that masturbation is permissible only if one is unmarried or is unable to marry, or to avoid fornication.
Those of the view that it is Haram (Forbidden, not allowed):
Ali al-Sistani, a 21st century Shi'a Twelver Islamic scholar on the question "If my wife wants me to masturbate in front of her, is it then allowed?":
You are not allowed to excite yourself with your own hands, but you can do it [to] your wife.
On the question "What does Islam say about masturbation? If a man is doing this what type of punishment will he deserve and how can he do\ get Tawbah?"
He has committed a forbidden act. Repentance would be sufficient for forgiveness.
And on the question "When I am unable to do Mut'ah (temporary marriage), am I allowed to masturbate?"
Masturbation is not permissible under any circumstances.
Hope answer of the question...