All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is an obligation on a person to cover his/her ‘Awrah (parts of the body that must be covered in Islam) from people who are not allowed to look at it, and it is disliked to be absolutely naked without a need. In fact, not being completely naked is a way of being shy from Allaah as the Prophet told Mu’aawiyah Ibn Haydah : “Cover your ‘Awrah except from your wife and whomever your right hand possesses.” Mu’aawiyah said, “O Prophet of Allaah, what if one of us is alone?” The Prophet said: “Allaah is worthier [has more right] to be shy from Him than from people.” [Abu Daawood, Ibn Maajah, At-Tirmithi and Ahmad]
Despite this, it is not a condition to cover one’s ‘Awrah for reciting the Quran and we are not aware of any Islamic evidence that prohibits reciting the Quran or Hadeeth when being naked. Nevertheless, it is desirable for a Muslim to be in a good appearance when he recites the Quran.
At-Tirmithi Al-Hakeem said in his book "Nawaadir Al-Usool": “Among the sacredness of the Quran is that one should wear clothes as if he were to enter upon the ruler; this is because (when reciting the Quran) he will be addressing [his Lord].”
Besides, Abul-‘Aaliyah used to wear a turban as well as his finest attire and face the Qiblah (direction of prayer) when he recited the Quran. Some scholars stated that among the etiquettes of reciting the Quran is that one should perform ablution, use the Miswaak (wooden tooth-stick) and wear his best clothes while being sedate and calm.
Also, it was reported that Imaam Maalik used to wear his best clothes, apply the best perfume that he had, and sit in the best position while being sedate and calm when he wanted to narrate the Hadeeth of the Prophet . This was to honor the Hadeeth of the Prophet and he would honor Islamic knowledge in general. Once he was asked a question, he said to the questioner, “Please wait.” Then, he performed ablution and then sat on his couch and said, “Laa hawla wa laa Quwwata illaa billaah” (There is no might, nor power, except by Allaah); and he would not issue a Fatwa except that he would start by saying this expression. Allaah Says (what means): {That [is so]. And whoever honors the symbols [i.e. rites] of Allaah — indeed, it is from the piety of hearts.}[Quran 22:32]
Therefore, it is good for whoever wants to recite the Quran or Hadeeth or Islamic knowledge in general to cover his ‘Awrah and not recite while being naked. It is known that the most unpleasant appearance of a person is when he/she is totally naked.
Allaah Knows best.