Short answer
Not by name. The only woman named in the Quran is Maryam. But Surah al-Nur, verses 11 to 26, was revealed about Aisha to declare her innocent of a slander spread about her. Scholars say this is one of her greatest honours.
The Sunni account is that the opening part of Surah al-Nur (24:11-26) was revealed to clear Aisha of the slander known as the Ifk. Anyone who accuses her of what these verses cleared her of rejects the Quran, according to the scholars.
The four schools agree on this.
Explanation
The Quran does not name Aisha, and it does not give her age: see Does the Quran say how old Aisha was? But a whole passage of Surah al-Nur is about her.
On the way back from an expedition, around 5 or 6 AH, Aisha left the camp to look for a lost necklace. The army moved on, thinking she was in her covered litter. A Companion, Safwan ibn al-Mu'attal, found her and brought her back on his camel. Hypocrites in Madinah, led by Abdullah ibn Ubayy, used this to spread a slander about her. For about a month the Prophet ﷺ received no revelation on it, and Aisha fell ill and wept day and night.
Then Allah revealed verses 11 to 26 of Surah al-Nur. They call the slander a lie, blame those who spread it, ask why the believers did not think well of one another, and declare the good innocent of what is said about them. Aisha said she had hoped for a dream that would clear her, never thinking that verses would be recited about her until the Last Day. Her story is told in full in Sahih al-Bukhari.
Scholars draw lessons from it: do not pass on rumours, think well of believers, and demand proof before an accusation. Muslims honour Aisha as a mother of the believers. Read her life on Aishah bint Abi Bakr.
The evidence
Quran, Surah An-Noor 24:11
إِنَّ ٱلَّذِينَ جَآءُو بِٱلْإِفْكِ عُصْبَةٌۭ مِّنكُمْ ۚ لَا تَحْسَبُوهُ شَرًّۭا لَّكُم ۖ بَلْ هُوَ خَيْرٌۭ لَّكُمْ ۚ لِكُلِّ ٱمْرِئٍۢ مِّنْهُم مَّا ٱكْتَسَبَ مِنَ ٱلْإِثْمِ ۚ وَٱلَّذِى تَوَلَّىٰ كِبْرَهُۥ مِنْهُمْ لَهُۥ عَذَابٌ عَظِيمٌۭ ﴿١١﴾
Indeed, those who came with falsehood are a group among you. Do not think it bad for you; rather it is good for you. For every person among them is what [punishment] he has earned from the sin, and he who took upon himself the greater portion thereof - for him is a great punishment.
The opening of the verses revealed about the slander against Aisha.
Quran, Surah An-Noor 24:12
لَّوْلَآ إِذْ سَمِعْتُمُوهُ ظَنَّ ٱلْمُؤْمِنُونَ وَٱلْمُؤْمِنَٰتُ بِأَنفُسِهِمْ خَيْرًۭا وَقَالُوا۟ هَٰذَآ إِفْكٌۭ مُّبِينٌۭ ﴿١٢﴾
Why, when you heard it, did not the believing men and believing women think good of one another and say, "This is an obvious falsehood"?
The believers should have rejected the rumour at once.
Quran, Surah An-Noor 24:26
ٱلْخَبِيثَٰتُ لِلْخَبِيثِينَ وَٱلْخَبِيثُونَ لِلْخَبِيثَٰتِ ۖ وَٱلطَّيِّبَٰتُ لِلطَّيِّبِينَ وَٱلطَّيِّبُونَ لِلطَّيِّبَٰتِ ۚ أُو۟لَٰٓئِكَ مُبَرَّءُونَ مِمَّا يَقُولُونَ ۖ لَهُم مَّغْفِرَةٌۭ وَرِزْقٌۭ كَرِيمٌۭ ﴿٢٦﴾
Evil words are for evil men, and evil men are [subjected] to evil words. And good words are for good men, and good men are [an object] of good words. Those [good people] are declared innocent of what the slanderers say. For them is forgiveness and noble provision.
Allah declares the good innocent of the slander.
Sahih al-Bukhari 4750
Sahih... إن الذين جاءوا بالإفك ...
"Indeed, those who came with the slander..."
Aisha's long account of the Ifk and the verses revealed about her.
Where the ruling is recorded
- Fath al-Bari (Ibn Hajar), Commentary on Kitab al-Tafsir, Surah al-Nur, the hadith of the Ifk. The fullest commentary on the event and its lessons.
- Sirat Ibn Hisham, Account of the expedition to Banu al-Mustaliq and the affair of the Ifk. The biographers' account of the event.
- Zad al-Ma'ad (Ibn al-Qayyim), Section on the expedition to Banu al-Mustaliq. Lessons and rulings drawn from the Ifk.
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.