Short answer
No. Reading with your eyes or in your mind is rewarded as looking at and reflecting on the Quran, but it is not recitation (tilawah). Recitation means forming the letters with your tongue, and the safer Hanafi view is that you should hear yourself. This matters most in salah, where reading only in your mind does not count.
Recitation (qira'ah) requires pronouncing the letters with the tongue; many Hanafi authorities add that the reciter must be able to hear himself, and this is the safer position. Reading only in the mind does not fulfil the recitation required in salah, though looking at the mushaf and reflecting is still rewarded. The four schools agree that reading only in the mind is not recitation.
The four schools agree on this.
Explanation
The Prophet ﷺ reported that Allah says: "I am with My servant when he remembers Me and his lips move with My mention." Ibn Abbas describes how, when revelation came, the Prophet moved his lips with it. Allah also tells him to recite the Quran with measured recitation (73:4). In each case recitation is something the tongue does.
In salah: even in the quiet prayers (Zuhr and Asr), you must move your tongue and lips to form the words of al-Fatiha and the surah. Someone who only reads in their head has not recited, so a prayer they pray alone or lead is not valid. If this has been your habit, see how to pray and ask a scholar about past prayers. The same applies to the dhikr after salah if you want its full reward.
When reading in your mind is useful: going over memorisation when you cannot speak, following a recitation with your eyes, and for someone who may not recite aloud at that time, such as a person who needs ghusl. Women's questions on this are in the women section. This kind of reading is reflection and is rewarded, but it is not counted as tilawah.
In a library or on a train, a whisper with moving lips is enough: no one else needs to hear you. See also reciting the Quran without wudu.
The evidence
Quran, Surah Al-Muzzammil 73:4
أَوْ زِدْ عَلَيْهِ وَرَتِّلِ ٱلْقُرْءَانَ تَرْتِيلًا ﴿٤﴾
Or add to it, and recite the Qur'an with measured recitation.
Recitation is described as an act of the tongue, measured and clear.
Quran, Surah Al-Qiyaama 75:16
لَا تُحَرِّكْ بِهِۦ لِسَانَكَ لِتَعْجَلَ بِهِۦٓ ﴿١٦﴾
Move not your tongue with it, [O Muhammad], to hasten with recitation of the Qur'an.
Shows that the Prophet recited by moving his tongue.
Sunan Ibn Majah 3792
Graded sahih... أنا مع عبدي إذا هو ذكرني وتحركت بي شفتاه ...
"I am with My servant when he remembers Me and his lips move with My mention."
Remembrance with the tongue is the form of dhikr and recitation.
Sahih al-Bukhari 5
Sahih... وكان مما يحرك شفتيه ...
"He used to move his lips with it."
The Prophet recited with movement of the lips.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Salah, chapter on the description of prayer, discussion of the lowest level of quiet recitation. The views of al-Karkhi and al-Hindwani on whether forming the letters is enough or one must hear oneself.
- al-Fatawa al-Hindiyya, Kitab al-Salah, chapter on recitation. Recitation requires correct pronunciation of the letters.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.