Short answer
No. A wet dream does not break the fast in any of the four schools, because it happens in sleep without your choice. You need to do ghusl before your next prayer, and your fast carries on. Waking up in a state of janabah (major impurity) after fajr does not affect the fast either.
A wet dream (ihtilam) does not break the fast and there is nothing to make up. Ghusl is fard for the next prayer, not for the fast. Someone in janabah from intercourse at night may begin the fast and do ghusl after fajr; delaying ghusl until a prayer time passes is sinful because of the missed prayer, not because of the fast.
The four schools agree on this.
Explanation
Accountability is lifted from a person while they sleep. A wet dream is entirely outside your control, so it has no effect on your fast, and the four schools agree on this. Do not feel guilty about it.
Ghusl. You must do ghusl before your next prayer. While fasting, rinse your mouth without gargling and draw water only into the soft part of the nose, so that nothing goes down your throat. See how to do ghusl and showering while fasting.
Janabah at dawn. Aisha reported that dawn would sometimes come while the Prophet ﷺ was in janabah from his wives; he would then do ghusl and fast. So if you had intercourse at night, or a wet dream before fajr, and did not have time for ghusl before dawn, your fast is still valid. Do ghusl in time to pray Fajr.
This is different from ejaculation while awake by your own action, which does break the fast. See does kissing break your fast for those cases.
The evidence
Sahih al-Bukhari 1925
Sahih... كان يدركه الفجر وهو جنب من أهله ...
"Dawn would come upon him while he was in janabah from his wives, then he would do ghusl and fast."
Being in janabah at the start of the fasting day does not harm the fast.
Sunan Abi Dawud 4398
Graded sahih... رفع القلم عن ثلاثة عن النائم حتى يستيقظ ...
"The pen is lifted from three: from the sleeper until he wakes up."
What happens in sleep without choice is not held against a person.
Where the ruling is recorded
- al-Hidaya, Kitab al-Sawm, chapter on what requires qada and kaffarah. A wet dream does not break the fast.
- Nur al-Idah with Maraqi al-Falah, Kitab al-Sawm, chapter on what does not break the fast. Ihtilam and waking in janabah do not break the fast.
- al-Majmu' (Nawawi), Kitab al-Siyam. Agreement of the schools that a wet dream does not break the fast.
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.