""This day I preferred your religion for you, and completed My favour upon you, and have chosen for you Islam as your religion" (5:3)
With the revelation of the above Koranic verse, it was virtually the end of the divine message through the Prophet Muhammad (may peace be on him), and therefore, also the closing of the office of Prophethood. But the Koran also more specifically declared: "Muhammad is not the father of any of your men, but he is the apostle of God and the last of the prophets (khatam al-Nabiiyyin), and God is cognizant of all things" (33:40). The words khatam al-nabiyyin and khatim al-nabiyyin means the last of the prophets, for both the words khatam and khatim mean the last portion of anything. Hence the doctrine of the finality of Prophethood in Muhammad (may peace be on him), therefore, rests on the clear words of the Koran.
The word khatam is derived from khatama, meaning to close a thing in such a manner that neither anything can enter in it, nor come out of it, or to close it or seal it. According to the Arabic usage, khatamal amala means to finish the work, and khatamal ina'a means to close the utensil and seal it, and khatamash shay means to finish anything to its end. Even in the Koran, the word khatama is used on several occasions: "On the day (of judgment) their mouth will be sealed, so that they will not be able to speak" (36:65) and "God has sealed their hearts and ears" (2:7), and "Sealed wine will be given to them to drink" (83:25).
The word khatam is also read with the up sound of t. Some scholars treat it as a verb, which means that the Prophet has sealed all prophets; while some say that it is a noun, which means that he is the end of all the prophets. Other scholars have read this word with the down sound of t which means that he was khatim in the sense of fa'il. In Persian it will mean the one who seals the prophets in which case also the meaning will be the same. The equivalent Persian word for khatam is muhr.
The end of the Prophethood is also proved from the following verse: "And those who believe in the revelation sent to thee, and sent before thy time" (2:4), and "O' you who believe, believe in God and His messenger and the scripture which He hath revealed unto His messenger and the scriptures which He revealed before him" (4:136)
Both these verses clearly speak of the messengers and the scriptures that had come before the Prophet, but do not refer to any messenger or scripture to come after him. Had there been a messenger or scripture even after him, it would have also been necessarily mentioned.