Reference: Fataawa Noor ‘alad-Darb – Question No.6324, Page 165, Volume 12
Question: We read the Qur.aan, and all Praise is due to Allaah [alone] we read a [complete] part (juz); so what is the ruling regarding the supplication we make after completing our recitation? Is this permissible or not?
Response: Allaah (‘Azza wa Jall) says:
And it is not from the guidance of the Prophet (sal-Allaahu ‘alayhi wa sallam) that he would supplicate upon finishing the recitation [of the Qur.aan]. Rather, it has been established that while ‘Abdullaah ibn Mas’ood (radhi-yAllaahu ‘anhu) recited from Soorah an-Nisaa, when he reached the aayah:
…the Prophet (sal-Allaahu ‘alayhi wa sallam) said:
And after this [recitation], the Messenger of Allaah (sal-Allaahu ‘alayhi wa sallam) did not supplicate, and nor did ‘Abdullaah ibn Mas’ood.
However, if [on the odd occasion] someone were to say a short supplication, such as: ‘All Praise is due to Allaah [alone], O Allaah accept this [recitation] from me’ – not that it is from the Sunnah to do so, and nor that it is something to be said regularly [after each recitation], then I anticipate there is no harm in that.
 Transmitted by al-Bukhaaree and Muslim.