In the Name of Allaah, the Most Gracious, the Ever Merciful…
At the end of Thul-Hijjah, the twelfth month of the Islamic calendar, some Muslims begin sharing messages with each other, with reminders to end the year with good deeds and begin the new year with obedience. Some observe the time as an opportunity for repentance and “setting things right”, similar to how the non-Muslims enter their new year by making “New Year’s resolutions”. Others may even go so far as to celebrate the event with special greetings, acts of worship like fasting, or festive gatherings.
THE ISLAMIC RULING ON OBSERVING THE ISLAMIC NEW YEAR
A question was posed to the Standing Committee for Fatwaa in Saudi Arabia about this issue, and their response was:
لا تجوز التهنئة بهذه المناسبات؛ لأن الاحتفاء بها غير مشروع
“It is not permissible to congratulate people on these occasions, since observing/celebrating them is not legislated.” 
Shaykh Saalih al-Fowzaan, one of the committee’s long-standing members, and widely recognized senior authority in Islamic verdicts, was asked, “There are some people who specify the year’s end as a time for special advice, admonitions or supplications. Are these actions correct?”
He -may Allaah preserve him- replied:
لا، هذا بدعة فلا يجوز أنه يخصص آخر السنة الهجرية بمعايدة أو بتهنئة أو بذكر أو بدعاء، ما يجوز هذا، ما كان السلف يفعلون هذا، نعم.
“No, this is bid’ah (innovation), it is not permissible to specify the end of the Hijri year as a holiday, or as a time for specific greetings, phrases of remembrance, or supplications. This is not permissible. The Salaf (early rightly-guided generations of Muslim predecessors) did not do this.” 
In one of his Friday sermons, Shaykh Saalih al-Fowzaan -may Allaah preserve him- gave a more detailed warning about the matter, saying:
عباد الله من البدع التي حدثت في هذا الزمان في هذا الوقت بالذات، ما ينشر في بعض الجولات، أو في الانترنت، أو يتناقله الناس في هذه الأيام التي هي آخر السنة الهجرية بداية السنة المقبلة، يوصون بعبادات ما أنزل الله بها من سلطان، يوصون الصيام في آخر العام، يوصون بالتوبة، يوصون بأشياء هذا ما أنزل الله به من سلطان لا يخص، لا تخص هذه الأيام بشيء لأنه لم يرد فيها دليل من الرسول صلى الله عليه وسلم، وكل محدثة بدعة، وكل بدعة ضلالة، فاحذروا من هذه الترويجات وهذه الشائعات وحذروا منها، فإنها شر وتجر إلى شرور، وإلى بدع أخرى، فلا يتساهل في أمر البدع…
Servants of Allaah! Among the innovations that have occurred in this day and age specifically is what is spread through cellphone messages or on the internet, and passed on by people [personally] among themselves as well, in these days at the end of the Hijri year and the beginning of the new one. They encourage certain acts of worship for which Allaah sent down no authority. They encourage fasting at the end of the year, as well as repentance and other matters which Allaah sent down no authority for. These days are not to be observed as anything special, as no evidence for this has come from the Messenger (may Allaah raise his rank and grant him peace). Every newly invented matter [in the Religion] is a bid’ah (innovation), and every innovation is misguidance. So be warned of these matters being promoted and spread, and warn [others] of them, as they are evil and drag [people] into other evil things and innovations. Lenience is not appropriate as it relates to matters of innovation… 
May Allaah reward Shaykh Saalih al-Fowzaan for these precise words of guidance and advice, about a matter of innovation that has crept into the ranks of the Muslims and actually grown in popularity over the years. It is not a matter that should be considered of little significance. Rather, our righteous early imaams warned us that considering some innovations to be small or minor can lead to disastrous results on a large scale.
IF IT IS NOT FROM ISLAM, WHERE IS IT FROM?
Upon realizing that observing the Hijri “New Year” is not from the Religion of Muhammad (may Allaah raise his rank and grant him peace), as understood and practiced by his Companions and the early Muslims, then where did it come from?
Just like many other innovations, it has come from the influence of other cultures and religions around us. You will notice around you that most -if not all- Western cultures today have a New Year’s celebration of one type or another. As is so common, such widespread practices are rooted in ancient pagan traditions. This one, observing the entrance of the new year, has been historically traced to a 4,000-year-old polytheist Babylonian pagan ritual, and Allaah’s Protection is sought:
When encountering this misguidance in the form of a greeting received from another Muslim, whether directly, or by phone or email, I would advise a kind and gentle response, like the following:
Dear brother [or sister], I assume you only intend good -may Allaah bless you-, but would you please take a moment to review this important information. [Link them to this article or one of similar clarity.]
And Allaah knows best.
Written by: Moosaa Richardson (1437/12/29)
Additional resource: Shaykh Saalih al-Fowzaan Warns Against Celebrating the Hijri New Year (Arabic/English) MP3 (Added 1438/12/30)
 Question #1 from Case #20795, as found at their official website: http://www.alifta.com/Fatawa/FatawaChapters.aspx?View=Page&PageID=151&PageNo=1&BookID=12
 Shaykh Saalih al-Fowzaan’s official website: http://www.alfawzan.af.org.sa/node/14214
 Shaykh Saalih al-Fowzaan’s official website: http://www.alfawzan.af.org.sa/node/13562