Honor Killing in Islam
Question

I would like to know what the ruling on Honor killings would be and how it should be punished according to the Laws of the Shar`iah.
Praise be to Allah.Is it lawful to shed the blood of a Muslim?
Killing a Muslim unlawfully is a serious matter and a grave crime. Allah says (interpretation of the meaning): 
“And whoever kills a believer intentionally, his recompense is Hell to abide therein; and the Wrath and the Curse of Allah are upon him, and a great punishment is prepared for him” [al-Nisa 4:93]
Al-Bukhari (6355) narrated from Ibn ‘Umar (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “The believer will continue to be encompassed by the mercy of Allah so long as he does not shed blood that it is forbidden to shed.” 
When can the blood of a Muslim be shed?
The Prophet (peace and blessings of Allah be upon him) has explained to us the reasons for which it becomes permissible to shed this blood. He said: “It is not permissible to shed the blood of a Muslim who bears witness that there is no god but Allah and that I am the Messenger of Allah except in three cases: a life for a life (murder), zina of one of who is previously-married (adultery), and the one who changes his religion and forsakes the jama’ah.” (Narrated by al-Bukhari, 6370) and Muslim, 3175) 
Conditions of killing an adulterer
From this it is clear that zina on the part of one who is married is one of the reasons that make it permissible to kill a person, but the adulterer cannot be killed unless two conditions are met: 

He should be previously-married. The scholars have explained what is meant by previously-married in this case. 

Zakariya al-Ansari (may Allah have mercy on him) said in Asna’l-Matalib (4/128): 
“The previously-married person, whether male or female, is any adult of sound mind who has previously had intercourse within a valid marriage.” 
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said in al-Sharh al-Zad (6/120): “There are five conditions for (being described as) previously-married: 

Intercourse
Within a valid marriage
Being an adult
Being of sound reason
Being free (i.e., not a slave).”  


The second condition is that it should be proven that the hadd punishment is deserved, by the testimony of four male witnesses who saw the private parts meet, or the person should freely admit to having committed zina, without being forced to do so. 

If it is proven that he deserves the hadd punishment, it is not permissible for individuals to carry out this punishment themselves. Rather the matter must be referred to the ruler or his deputy to prove the crime and carry out the punishment, because if individuals carry out hadd punishments, that will lead to a great deal of corruption and evil. 
Ibn Muflih al-Hanbali (may Allah have mercy on him) said in al-Furu’ (6/53): 
“It is haram for anyone to carry out a hadd punishment except the ruler or his deputy.”
This is something on which the jurists of Islam are unanimously agreed, as was stated in al-Mawsu’ah al-Fiqhiyyah (5/280): 
“The jurists are unanimously agreed that the one who should carry out hadd punishments is the ruler or his deputy, whether the punishment is transgressing one of the limits of Allah, may He be exalted, such as zina, or a transgression against another person, such as slander.”
Concealing one who has committed this evil deed so that he may repent and set his affairs straight before he dies is better than exposing him, let alone killing him. The Prophet (peace and blessings of Allah be upon him) turned away from Maa’iz (may Allah be pleased with him) after he admitted committing zina, and he ignored him until he had repeated his confession several times, then he carried out the hadd punishment on him. 
Is honor killing halal?
Based on this, that which is called “honor killing” is a transgression and wrongdoing, because it is killing one who does not deserve to be killed, namely the virgin if she commits zina (fornication), but the shar’i punishment in her case is flogging and banishment for one year, not execution. Prophet Muhammad (peace and blessings of Allah be upon him) said: “(The punishment for zina) of a virgin with a virgin person is one hundred lashes and exile for one year.” (Narrated by Muslim) 
The one who kills her has killed a believing soul whom Allah has forbidden to be killed, and there is a stern warning concerning that, as Allah, may He be glorified and exalted, says (interpretation of the meaning): 
“And those who invoke not any other ilah (god) along with Allah, nor kill such person as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse - and whoever does this shall receive the punishment. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace.” [al-Furqan 25:68-69]
Even if we assume that she deserves to be executed (if she was previously-married and committed zina), no one should do that but the ruler – as stated above. 
Moreover, in many cases killing is done on the basis of accusations and speculation, without proving whether the immoral action even took place. 
And Allah knows best.