Shaking Hands of Non-Mahram Women
15-7-2004 | IslamWeb
Question:
Why does Islam not allow greeting non-Mahram women by hand?
Answer:
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Shaking hands of women is of two kinds:
1. Shaking the hands of Mahram (unmarriageable women) is permissible, for the Hadeeth that the Prophet, sallallaahu ‘alayhi wa sallam, used to kiss Faatimah 
(who was his daughter) when she came to him and she used to kiss him when he came to her. Since touching the Mahram in the mentioned way is lawful, shaking hands is a kind of touching and it is permissible or even desirable with Mahrams.
2. Shaking the hands of non-Mahram women (marriageable women) is of two kinds. Firstly, if a woman is very advanced in age, neither does she have sexual desire nor do men incline to her, then it is permissible to shake hands with her, since there is no sexual desire from both sides. The prohibition is for the existence of sexual temptation. As long as there is no temptation, it is lawful. However, the Scholars of the Shaafi’i School prohibited shaking hands with such a woman for the general evidence of the Hadeeth, and they did not make any exception.
Secondly, if a woman is young, then shaking hands with her is strictly prohibited according to the four Schools of jurisprudence, and the Hanbali School said whether or not the shaking is with a partition. The Prophet, sallallaahu ‘alayhi wa sallam, said: “If one of you were to be stabbed in the head with an iron needle, it would be better for him than touching a woman whom he is not permitted to touch.” There is no doubt that shaking hands is a form of touching.
Aa’ishah said: “I swear by Allah, the hand of the Prophet, sallallaahu ‘alayhi wa sallam, never touched the hand of any woman, but he only used to take their pledge of allegiance orally. I swear by Allah, the Prophet did not take the pledge of allegiance of the women except in accordance with what Allah had ordered him. When he accepted their pledge of allegiance he would say to them, “I have accepted your oath of allegiance orally.”
Imaam An-Nawawi 
said: “The Scholars of the Shaafi’i School said that if it is forbidden to look at someone, it is forbidden to touch her; rather, touching is more serious than looking because looking at a non-Mahram woman is permissible if one wants to marry her, but touching her is prohibited.”
Allah Knows best.