Substantial evidence has been provided that Muhammad was not only literate, but also wrote the original Quran with his own hand. A detailed argument can be found here.
It was Muhammad’s sole duty to deliver God’s final scripture to mankind. If he outsourced the critical task of physically writing the revelations he received from God during the 23 years he received Quranic revelations, then he would have been neglecting his very function as prophet.
[42:48] If they turn away, we did not send you as their guardian. Your sole mission is delivering the message.
[64:12] You shall obey GOD and you shall obey the messenger. If you turn away, then the sole mission of our messenger is to deliver the message.
An additional confirmation that Muhammad wrote the Quran with his own hand can be found in 69:45 of the Quran.
[69:44] Had he uttered any other teachings. [69:45] We would have punished him [by the right hand]. [69:46] We would have stopped the revelations to him. [69:47] None of you could have helped him.
وَلَو تَقَوَّلَ عَلَينا بَعضَ الأَقاويلِ
لَأَخَذنا مِنهُ بِاليَمينِ
ثُمَّ لَقَطَعنا مِنهُ الوَتينَ
فَما مِنكُم مِن أَحَدٍ عَنهُ حاجِزينَ
Here is a word for word breakdown of 69:45
The word ” بِالْيَمِينِ ” means: by the right hand. It comes from the root ” ي م ن “. The meaning of this root is the following:
to meet on the right side; bless; lead to the right; be a cause of blessing; right hand; oaths; blessed; peoples of the right hands that are blessed
Why would God indicate that had Muhammad taught any other teachings other than the Quran that He would have seized him, Muhammad, “by the right hand”?
The context of 64:44 – 47 are in reference to God’s revelations of the Quran, that was given to Muhammad to deliver. To provide assurances that God’s verses were not altered by the messenger, God is telling us that if Muhammad was to write any other teachings He would have seized his right hand, thus refraining him from being able to write any more of God’s revelations.
In 17:73 – 75, God gives us further assurances that the Quran, that Muhammad wrote with his own hand, was exactly as intended by God without alteration by any intermediary.
[17:73] They almost diverted you from the revelations we have given you. They wanted you to fabricate something else, in order to consider you a friend. [17:74] If it were not that we strengthened you, you almost leaned towards them just a little bit. [17:75] Had you done that, we would have doubled the retribution for you in this life, and after death, and you would have found no one to help you against us.