It is not prescribed to do a single prostration for the sake of du`a’
Question

Some people, when they want to offer du`a after praying, prostrate and offer du`a whilst prostrating. Is this prostration Sunnah?.
Praise be to Allah.Islam does not prescribe drawing close to Allah by means of prostration unless the prostration is in the prayer (salaah) or for a specific reason, such as prostration of forgetfulness (sujood al-sahw, if a mistake is made in the prayer), or prostration of recitation (sujood al-tilaawah, required when reading certain verses of the Qur’aan), or the prostration of gratitude (sujood al-shukr).  
As for prostration for the sake of du`a, there is nothing in sharee’ah to indicate that it is permissible or mustahabb. Rather what is proven from the Prophet (blessings and peace of Allah be upon him) in many mutawaatir hadeeths is that he used to raise his hands in du`a, and he encouraged others to do so. He said: “Your Lord, may He be blessed and exalted, is characterized by modesty and generosity, and He is so Kind to His slave that, if His slave raises his hands to Him, He does not let him take them back empty.” Narrated by Abu Dawood (1488); classed as saheeh by al-Albani in Saheeh Abi Dawood. 
So prostrating for the sake of du`a is an innovation, because the Prophet (blessings and peace of Allah be upon him) did not do it, and because it is forsaking the Sunnah that the Prophet (blessings and peace of Allah be upon him) encouraged, which is raising the hands in du`a. 
These scholars denounced this single prostration and forbade it. It was mentioned by Abu Shaamah (may Allah have mercy on him) in his book al-Baa’ith ‘ala Inkaar al-Bida’ wa’l-Hawaadith (p. 62, 63) and he said: Imam al-Haramayn Abu’l-Ma’aali said: The author of al-Taqreeb mentioned from some of his companions that if a man submits to Allah and prostrates for no reason, he may do that, and I have not seen this except with him. My Shaykh regarded that as makrooh, and objected strongly to anyone who did that. He said: this is my view. 
Abu Haamid al-Ghazali said: Shaykh Abu Muhammad (may Allah have mercy on him) objected strongly to the one who did that, and this is the correct view. He said in Kitaab al-Nadhr: No one was of the view that prostration on its own becomes obligatory if one makes a vow to do that, because it is not an act of worship for which there is a reason, such as recitation (i.e., prostration of recitation). 
Imam al-Haramayn said: My Shaykh was of the definite opinion that prostration on its own does not become obligatory if one makes a vow to do that, even though the reciter of the Qur’aan may prostrate, but prostration on its own for no reason is not an act of worship according to the correct view.  
The author of al-Tatimmah said: Some people have the habit of prostrating after they finish the prayer and saying du`a whilst doing so. He said: We know of no basis for this prostration and it was not narrated from the Messenger of Allah (blessings and peace of Allah be upon him) or from his Companions. It is better to offer du`a during the prayer, because of the reports that have been narrated concerning that. And Allah knows best. 
I (Abu Shaamah) say: The fact that prostration is an act of worship within prayer does not necessarily mean that it is an act of worship outside of prayer, like bowing. Al-Faqeeh Abu Muhammad said: Islam does not say that one may draw close to Allah by doing a single prostration for which there is no reason. End quote. 
See also question no. 98156 .