Minecraft asset (audio) permissions under these guidelines:
- NOT make people think that you or what you are doing is official; approved or endorsed by us; or associated or connected with us;
- NOT be unlawful, deceptive, obscene, harmful or disparaging;
- NOT take action that would harm or damage any of our Brands or any of our Assets;
- NOT include anything else around it that makes people think that you or what you are doing is official; approved or endorsed by us; or associated or connected with us;
- do so in a way that honestly and fairly describes those things or the purpose of them;
- ensure that the Name (which includes any confusingly similar name) is not the first word, doesn't use any - other aspect of any of our Brands or Assets as part of any related branding, including as or as part of any logo;
- make it clear that the product is unofficial and not from Minecraft or approved by Minecraft.
tl;dr
- credit the music author, not Minecraft
- can't promote the game as "having music from Minecraft" or implying partnership or official ties with Minecraft
- can't use their content as promotion for the game itself
Follow those, and you can technically use Minecraft's music in-game, since Minecraft is ok with its use in non-commercial ventures under these guidelines. Can read more about it here.
https://account.mojang.com/documents/brand_guidelines