Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Muslims, men and women, must observe shyness in all their correspondence and conversations. 2- Islam does not forbid women from talking to men nor men to women if the situation calls for it and the conversation abides by the boundaries of the Islamic Shari`ah.
In response to the question in point, the European Council for Fatwa and Research issued the following Fatwa:
In the authentic Hadith of the Prophet Muhammad (peace and blessings be upon him), he said, “Shyness is part of your faith.” (Al-Bukhari and Muslim)
In another Hadith, the Prophet says, “Shyness brings only good.” (Al-Bukhari and Muslim)
This shyness is a beautiful manner for both men and women, but more so for women, because it agrees with their feminine nature. That is why women do not initiate a conversation with strange men.
However, traditions and customs govern this matter, and these change from one country to another, from one time to another and from one situation to another.
Nevertheless, it is important to realize that Islam does not forbid women from talking to men, nor men to women if the situation calls and the conversation abides by the boundaries of the Islamic Shari`ah.
Allah Almighty addressed the wives of the Prophet Muhammad (peace and blessings be upon him) saying, “O wives of the Prophet! You are not like any other women. If you keep your duty to Allah, then be not soft in speech, lest he in whose heart is a disease should be moved with desire, but speak in an honorable manner.” (Al-Ahzab 33:32)
Thus, despite the special position and laws which govern them alone and which place more restrictions upon them than any other, Islam did not prevent the Prophet’s wives from speech, but forbade them to speak in such a way which would move those with illness in their hearts with desire and lust.
However, honorable and reasonable speech falls within Islam as stated by the previous verse. There are many Hadiths which confirm the permissibility of men greeting women and women greeting men, as well as the lawfulness of men visiting sick women and vice versa.
But this does not imply the lifting of all boundaries so that women start speaking to all men who come and go or that men start speaking to all women, as this is rejected by logic and good taste before being rejected by Islam. It is permissible for a woman to speak to a male relative, a teacher, a neighbor, a supervisor at work, and others according to the requirements and needs of everyday life and complex relations amongst people in our days, as long as trust is established, troubles (fitnah) are restrained, and conditions are normal.
Indeed, the custom in many Islamic countries is for men to greet women and for women to greet men when they meet. They also exchange conversation (honorable speech) regarding important and relevant matters, all with the approval of fathers, husbands and brothers as well as the scholars.
We do not deny that some countries have very strict traditions regarding women so that they become more like prisoners in their own homes until death comes to them. However, even though some scholars may agree with this, it remains that clear, covert and correct legal evidence contradicts these traditions in addition to the objectives of Shari`ah, the interests of mankind, and the development of age and people.
Allah Almighty knows best.
Excerpted, with slight modifications, from, http://www.ecfr.org