As of Android 6.0, the majority of the IPv6 protocol seems to be supported with significant parts missing such as DHCPv6.
Check Issue #36908577 Support IPv6 for more info, specifically the issues listed in comment #105:
Enhancement: Support for DHCPv6 (RFC 3315) Won't Fix (Intended behavior)
http://code.google.com/p/android/issues/detail?id=32621
Enhancement: Support for Recursive DNS Server Option in ICMPv6 Router Advertisements (RFC 6106) Fixed
http://code.google.com/p/android/issues/detail?id=32629
Enhancement: Support connecting to IPv6-only wireless networks Fixed
http://code.google.com/p/android/issues/detail?id=32630
Defect: APN Protocol ignored when roaming Fixed
http://code.google.com/p/android/issues/detail?id=32631
Enhancement: Automatic fallback from IPv4/IPv6 APN Protocol to parallel IPv4 + IPv6 Won't Fix (Obsolete)
http://code.google.com/p/android/issues/detail?id=32632
Defect: Frequently ignores ICMPv6 RAs and other multicast traffic Won't Fix (Obsolete)
http://code.google.com/p/android/issues/detail?id=32662
(Consider reading the issues and their comments carefully, because while some of them have their status updated to "fixed", some users were reporting they still have the same issues.)