It is not prescribed to face towards the grave of the Prophet (blessings and peace of Allah be upon him) when offering du ‘aa’ (supplication)
Question

                In the Prophet’s Mosque I saw some people facing towards the grave of the Prophet (blessings and peace of Allah be upon him)) when offering supplication, and raising their hands. Is this Sunnah?
Praise be to Allah.
    What some visitors and others do, of 
    striving to offer du‘aa’ at the grave of the Prophet (blessings and peace of 
    Allah be upon him), turning to face towards the grave and raising their 
    hands in supplication, is contrary to the way of the righteous early 
    generations, the companions of the Messenger of Allah (blessings and peace 
    of Allah be upon him) and those who followed them in truth. 

    Rather it comes under the heading of 
    innovations that have been introduced into the religion. The Prophet 
    (blessings and peace of Allah be upon him) said: “I urge you to adhere to my 
    Sunnah and the way of the Rightly-Guided Caliphs who come after me. Adhere 
    to it and cling firmly to it. And beware of newly introduced matters, for 
    every newly introduced matter is an innovation, and every innovation (in 
    religion) is a going astray.” Narrated by Abu Dawood and an-Nasaa’i with a 
    hasan isnaad. And he (blessings and peace of Allah be upon him) said: 
    “Whoever introduces anything into this matter of ours that is not part of 
    it, it will be rejected.” Narrated by al-Bukhaari and Muslim. According to a 
    version narrated by Muslim: “Whoever does an action that is not in 
    accordance with this matter of ours, it will be rejected.” 

    ‘Ali ibn al-Husayn Zayn al-‘Aabideen (may 
    Allah be pleased with him) saw a man offering du‘aa’ at the grave of the 
    Prophet (blessings and peace of Allah be upon him) and he told him not to do 
    that and said: Shall I not tell you a hadeeth that I heard from my father, 
    from my grandfather, from the Messenger of Allah (blessings and peace of 
    Allah be upon him), that he said: “Do not take my grave as a place of 
    regular visitation, and do not make your houses graves. Send blessings upon 
    me, for your salaams will reach me no matter where you are.” Narrated by al-Haafiz 
    Muhammad ibn ‘Abd al-Waahid al-Maqdisi in his book, al-Ahaadeeth al-Mukhtaarah. 

    The same applies to what some visitors do 
    when sending salaams upon him, namely placing the right hand on the left 
    hand on or below the chest, as is done in the prayer. This is not 
    permissible when sending salaams upon the Prophet (blessings and peace of 
    Allah be upon him) or when greeting anyone else, such as kings, leaders and 
    so on, because it is a posture of humility, submission and worship, and is 
    not befitting except for Allah, as al-Haafiz Ibn Hajar (may Allah have mercy 
    on him) narrated from the scholars in (his book) al-Fath. This matter 
    is quite clear for the one who reflects on it, and whose aim is to follow 
    the guidance of the righteous early generations. 

    With regard to the one who is overwhelmed 
    by partisan feelings, and whims and desires, blind imitation and suspicion 
    towards those who call people to follow the practice of the righteous early 
    generations, his case is for Allah to judge. We ask Allah to guide us and 
    him, and to help us all to give precedence to the truth over all else, for 
    He, may He be glorified, is the best to be asked. End quote. 

    Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah 
    have mercy on him.