Short answer
No. Listening to music does not break the fast in any of the four schools, because nothing enters the body. But in the mainstream Hanafi position music with instruments is haram, and a sin committed while fasting takes away from the reward of the fast.
The fast stays valid. Listening to music with instruments is haram in the relied-upon Hanafi position, and doing it while fasting is worse, since the fast is meant to guard the ears and the tongue as well as the stomach. Nasheeds without instruments and with clean words are allowed.
The four schools agree on this.
Explanation
The fast is broken by things that enter the body through the mouth or another open passage, and by intercourse. Sound reaching the ears is neither, so music, a podcast or an advert you hear has no effect on the validity of your fast. The four schools agree on this.
The reward is another matter. The Prophet ﷺ called the fast a shield and told the fasting person not to speak obscenely or behave foolishly. The scholars explain that a complete fast is a fast of the whole body: the eyes, ears and tongue fast along with the stomach. A fast kept while doing what is haram is valid, but much of its reward can be lost.
Is music haram? The Hanafi school, with most classical scholars, holds that musical instruments are haram, based on hadith such as the one in Sahih al-Bukhari about people who would treat musical instruments as lawful. Some scholars, past and present, allow some music with clean lyrics and question the strength of that evidence. For the reasoning, see why music is haram in Islam. Music you hear without choosing it, in a shop or a taxi, is not held against you: see hearing music in public.
What to listen to instead. Ramadan is the month of the Quran. Swap playlists for recitation, a tafsir series or nasheeds without instruments. If you slipped and listened to music while fasting, your fast is still valid: make istighfar and carry on.
The evidence
Quran, Surah Luqman 31:6
وَمِنَ ٱلنَّاسِ مَن يَشْتَرِى لَهْوَ ٱلْحَدِيثِ لِيُضِلَّ عَن سَبِيلِ ٱللَّهِ بِغَيْرِ عِلْمٍۢ وَيَتَّخِذَهَا هُزُوًا ۚ أُو۟لَٰٓئِكَ لَهُمْ عَذَابٌۭ مُّهِينٌۭ ﴿٦﴾
And of the people is he who buys the amusement of speech to mislead [others] from the way of Allah without knowledge and who takes it in ridicule. Those will have a humiliating punishment.
Ibn Mas'ud and other early scholars explained this idle talk as singing, one basis of the Hanafi position on music.
Sahih al-Bukhari 5590
Sahih... ليكونن من أمتي أقوام يستحلون الحر والحرير والخمر والمعازف ...
"There will be people from my nation who treat as lawful fornication, silk, wine and musical instruments."
Musical instruments are listed with things that are haram.
Sahih al-Bukhari 1894
Sahih... الصيام جنة فلا يرفث ولا يجهل ...
"Fasting is a shield, so let him not speak obscenely or act foolishly."
The fasting person guards his behaviour, not only his stomach.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Sawm, chapter on what breaks the fast and what does not. The fast is broken by what reaches the body cavity through an open passage, not by what is heard.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Hazr wa al-Ibaha. Listening to musical instruments is sinful.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. 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.