If I open the Minecraft launcher on a host with IPv4 turned off, only IPv6, then the launcher goes into offline mode. If I try to join a LAN multiplayer session, I am refused with the message "Failed to login: The authentication servers are currently down for maintenance". It is possible to connect and play over IPv6 if IPv4 is also connected, but at the moment IPv6-only cannot authenticate.
Also the launcher cannot download jar files over IPv6 (MCL-2627), and LAN multiplayer sessions do not appear in scan (MC-92923)
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I'm not very familiar with the various servers required for a minecraft session. I think in addition to the authentication server (authserver.mojang.com), there is the session server (sessionserver.mojang.com), and the skin server (???), as well as the main web portal minecraft.net, where you change your skin and username. Eventually one will want all four of them to be accessible over IPv6. Right now none of them has an AAAA DNS record.

I think the services are listed at the mojang help page: https://help.mojang.com/customer/en/portal/articles/1452251-minecraft-java-edition-services
minecraft.net
account.mojang.com
authserver.mojang.com
sessionserver.mojang.com
skins.minecraft.net
textures.minecraft.net
Ideally an IPv6 infrastructure change would address all six of these Mojang servers simultaneously, as well as switching over to IPv6 on Amazon Web Services for downloading JAR files, as per WEB-632.

This following technique requires using MultiMC5 (an alternative Minecrft launcher) which use IPv6 by default for authenticating with the Mojang auth servers because the official Minecraft launcher just doesn't lookup for AAAA records when launching it.
Thanks to AWS CloudFront you can force Minecraft and MultiMC5 to use IPv6 servers by adding those entries into your hosts file:
2600:9000:2012:: account.mojang.com
2600:9000:2012:: authserver.mojang.com
2600:9000:2012:: api.mojang.com
2600:9000:2012:: sessionserver.mojang.com
2600:9000:2012:: skins.minecraft.net
2600:9000:2012:: textures.minecraft.net
The IPv6 address 2600:9000:2012:: is an IPv6 address from the range of Amazon Web services and not a random subnet. You may check that by typing the address into your favorite search engine.
I hope this help Minecraft players behind NAT64/IPv6 only networks.

Hello, we've invested a bit of time in this and come to the conclusion that we won't be supporting IPv6 in the foreseeable future. We have balanced being backward compatible with older operating systems, the time needed to validate that the new protocol works, as well as the benefits that this gives.
Minecraft is still seeing IPv6 issues (see MC-232009 and JDK-8272996). Until we reach a point where all our games, launchers, dependencies and supported operating systems fully work with IPv6 we won't be turning it on for any of our endpoints. For the time being, we won't be fixing this.
I have read that turning on IPv6 on a heavy traffic public server is risky; if you add an IPv6 address and an AAAA record with the same CNAME, then there is a risk that misconfigured hosts will try to connect to the IPv6 address and fail, leading to long load times, or no load at all, either way a bad user experience. It's why Google started out by turning on IPv6 only a little at a time, only for ISPs known to work with IPv6 (see [DNS whitelisting](https://en.wikipedia.org/wiki/IPv6_brokenness_and_DNS_whitelisting)). Then participated in those IPv6 day holidays a few years back. I believe many major internet hosts are now serving AAAA DNS queries to everyone, so it may be safe for Mojang to do so too, but I'm not a professional, so take these beliefs with a grain of salt.
The other option is to set a separate CNAME like ipv6.authserver.mojang.com or whatever, with only an AAAA record, no A record. The client can have an option to prefer one or the other, set by the user. This might be safer in the short run, but it's also more work, and in the long run we should be preparing all infrastructure to be dual stack.