Praise be to Allah.
For a man to shake hands with a non-mahram woman (one to whom he is not related) is haraam and is not permitted at all. Among the evidence for this is the hadeeth of Ma’qal ibn Yassaar (may Allaah be pleased with him) who said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘If one of you were to be struck in the head with an iron needle, it would be better for him than if he were to touch a woman he is not allowed to.”(Reported by al-Tabaraani; classed as saheeh by al-Albaani in Saheeh al-Jaami’, 5045).
There is no doubt that for a man to touch a non-mahram woman is one of the causes of fitnah (turmoil, temptation), provocation of desire and committing haraam deeds. No one should say that their intention is sound or their heart is clean, because the one who was the purest of heart and the most chaste of all, the Messenger of Allaah (peace and blessings of Allaah be upon him) never touched a non-mahram woman, even when accepting bay’ah (oath of allegiance) from women. He did not hold their hands when accepting their bay’ah, as he did with men; their bay’ah was by words only, as was reported by his wife ‘Aa’ishah (may Allaah be pleased with her). She said that the Messenger of Allaah (peace and blessings of Allaah be upon him) would test the believing women who emigrated to him with the aayah (interpretation of the meaning): “O Prophet! When believeing women come to you to give you the bay’ah (pledge), that they will not associate anything in worship with Allaah, that they will not steal, that they will not commit illegal sexual intercourse, that they will not kill their children, that they will not utter slander, intentionally forging falsehood (i.e., by making illegal children belong to their husbands), and that thye will not disobey you in any ma’ruf (Islamic monotheism and all that which Islam ordains), then accept their bay’ah and ask Allaah to forgive them. Verily Allaah is Oft-Forgiving, Most Merciful.” [al-Mumtahinah 60:12] ‘Aa’ishah said: “So whoever of the believing women agreed to these conditions, the Messenger of Allaah (peace and blessings of Allaah be upon him) would say to her: ‘I have accepted your bay’ah by words.’ By Allaah, his hand never touched the hand of any woman when accepting their bay’ah; he accepted their bay’ah by saying ‘I have accepted your bay’ah on this basis.’”
(Reported by al-Bukhaari, 4512; according to another report: he accepted their bay’ah by words… the hand of the Messenger of Allaah (peace and blessings of Allaah be upon him) never touched the hand of any woman except a woman he owned . Reported by al-Bukhaari, 6674).
Some Muslims feel too embarrassed to refuse when a woman offers her hand to them. In addition to mixing with women, some of them claim that they are forced to shake hands with fellow-students and teachers in schools and universities, or with colleagues in the workplace, or in business meetings and so on, but this is not an acceptable excuse. The Muslim should overcome his own feelings and the promptings of the Shaytaan, and be strong in his faith, because Allaah is not ashamed of the truth. The Muslim could apologize politely and explain that the reason he does not want to shake hands is not to offend or hurt anybody’s feelings, but it is because he is following the teachings of his religion. In most cases this will earn him respect from others. There is no harm done if they find it strange at first, and it may even be a practical opportunity for da’wah. And Allaah knows best.