Shaykh Yusuf al-Qaradawi on shaking hand with women

Firstly, shaking hands between males and females who are not mahrams is only permissible when there is no desire or fear of fitnah. But if there is fear of fitnah, desire, or enjoyment, then handshaking is no doubt haram (unlawful). In contrast, if either of these two conditions (that there is no desire or fear of fitnah) is lacking between a male and any of his female mahrams, such as his aunt or foster sister or the like, then handshaking will be haram (although it is originally permissible).
Secondly, handshaking between males and females who are not mahrams should be restricted to necessary situations such as between relatives or those whose relationships are established by marriage. It is preferable not to expand the field of permissibility in order to block the means to evil and to be far away from doubt and to take the Prophet (peace and blessings be upon him) as a model when there is no proof that he shook hands with a non-mahram woman. Also, it is preferable for the pious Muslim, male or female, not to stretch out his/her hand to shake the hand of anyone of the opposite sex who is not mahram. But if he/she is put in a situation that someone stretches out his/her hand to shake hands with him/her, then he/she can do that.
I have tried to clarify the detailed ruling of the issue here in order to inform those who are in the dark about it how to behave while sticking to the tenets of their religion. Also, when the detailed Islamic ruling is explained and people are fully aware of it, there will be no room for personal justifications that are not supported by legal backing.

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