Re-creation steps:

0) Setup host that supports ipv6
1) Install the ActiveDirectory plugin
2) Load /configureSecurity/
3) Choose 'Active Directory' for the Security Realm
4) Put in an arbitrary 'Domain Name'
5) Click Test

This results in the following stacktrace, indicating it only supports ipv4 addresses because of the NumberFormatException:

javax.servlet.ServletException: java.lang.NumberFormatException: For input string: "db00:eef0:a52::"
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:778)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:858)
at org.kohsuke.stapler.MetaClass$6.doDispatch(MetaClass.java:248)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:728)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:858)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:631)
at org.kohsuke.stapler.Stapler.service(Stapler.java:225)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:848)
at org.eclipse.jetty.servlet.ServletHolder.handle(ServletHolder.java:686)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1494)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:96)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:88)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:48)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.UnwrapSecurityExceptionFilter.doFilter(UnwrapSecurityExceptionFilter.java:51)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:117)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.providers.anonymous.AnonymousProcessingFilter.doFilter(AnonymousProcessingFilter.java:125)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.rememberme.RememberMeProcessingFilter.doFilter(RememberMeProcessingFilter.java:142)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.AbstractProcessingFilter.doFilter(AbstractProcessingFilter.java:271)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.basicauth.BasicProcessingFilter.doFilter(BasicProcessingFilter.java:174)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ApiTokenFilter.doFilter(ApiTokenFilter.java:74)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.context.HttpSessionContextIntegrationFilter.doFilter(HttpSessionContextIntegrationFilter.java:249)
at hudson.security.HttpSessionContextIntegrationFilter2.doFilter(HttpSessionContextIntegrationFilter2.java:67)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:164)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at org.kohsuke.stapler.compression.CompressionFilter.doFilter(CompressionFilter.java:46)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1474)
at org.eclipse.jetty.servlet.ServletHandler.doHandle(ServletHandler.java:499)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:137)
at org.eclipse.jetty.security.SecurityHandler.handle(SecurityHandler.java:533)
at org.eclipse.jetty.server.session.SessionHandler.doHandle(SessionHandler.java:231)
at org.eclipse.jetty.server.handler.ContextHandler.doHandle(ContextHandler.java:1086)
at org.eclipse.jetty.servlet.ServletHandler.doScope(ServletHandler.java:428)
at org.eclipse.jetty.server.session.SessionHandler.doScope(SessionHandler.java:193)
at org.eclipse.jetty.server.handler.ContextHandler.doScope(ContextHandler.java:1020)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:135)
at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:116)
at org.eclipse.jetty.server.Server.handle(Server.java:370)
at org.eclipse.jetty.server.AbstractHttpConnection.handleRequest(AbstractHttpConnection.java:489)
at org.eclipse.jetty.server.AbstractHttpConnection.content(AbstractHttpConnection.java:960)
at org.eclipse.jetty.server.AbstractHttpConnection$RequestHandler.content(AbstractHttpConnection.java:1021)
at org.eclipse.jetty.http.HttpParser.parseNext(HttpParser.java:865)
at org.eclipse.jetty.http.HttpParser.parseAvailable(HttpParser.java:240)
at org.eclipse.jetty.server.AsyncHttpConnection.handle(AsyncHttpConnection.java:82)
at org.eclipse.jetty.io.nio.SelectChannelEndPoint.handle(SelectChannelEndPoint.java:668)
at org.eclipse.jetty.io.nio.SelectChannelEndPoint$1.run(SelectChannelEndPoint.java:52)
at winstone.BoundedExecutorService$1.run(BoundedExecutorService.java:77)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
at java.lang.Thread.run(Thread.java:745)
Caused by: java.lang.NumberFormatException: For input string: "db00:eef0:a52::"
at java.lang.NumberFormatException.forInputString(NumberFormatException.java:65)
at java.lang.Integer.parseInt(Integer.java:580)
at java.lang.Integer.parseInt(Integer.java:615)
at com.sun.jndi.dns.DnsClient.<init>(DnsClient.java:127)
at com.sun.jndi.dns.Resolver.<init>(Resolver.java:61)
at com.sun.jndi.dns.DnsContext.getResolver(DnsContext.java:573)
at com.sun.jndi.dns.DnsContext.c_getAttributes(DnsContext.java:434)
at com.sun.jndi.toolkit.ctx.ComponentDirContext.p_getAttributes(ComponentDirContext.java:235)
at com.sun.jndi.toolkit.ctx.PartialCompositeDirContext.getAttributes(PartialCompositeDirContext.java:141)
at com.sun.jndi.toolkit.ctx.PartialCompositeDirContext.getAttributes(PartialCompositeDirContext.java:129)
at javax.naming.directory.InitialDirContext.getAttributes(InitialDirContext.java:142)
at hudson.plugins.active_directory.ActiveDirectorySecurityRealm$DescriptorImpl.doValidate(ActiveDirectorySecurityRealm.java:303)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:483)
at org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:298)
at org.kohsuke.stapler.Function.bindAndInvoke(Function.java:161)
at org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:96)
at org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:120)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:728)
... 63 more