UnsupportedClassVersionError is thrown while adding user.

The server can be successfully started, but I'm unable to manage it because running add-user.bat immediately fails with the following error:

Exception in thread "main" java.lang.UnsupportedClassVersionError: org/jboss/as/domain/management/security/adduser/AddUser : Unsupported major.minor version 51.0
at java.lang.ClassLoader.defineClass1(Native Method)
at java.lang.ClassLoader.defineClassCond(ClassLoader.java:631)
at java.lang.ClassLoader.defineClass(ClassLoader.java:615)
at org.jboss.modules.ModuleClassLoader.doDefineOrLoadClass(ModuleClassLoader.java:361)
at org.jboss.modules.ModuleClassLoader.defineClass(ModuleClassLoader.java:482)
at org.jboss.modules.ModuleClassLoader.loadClassLocal(ModuleClassLoader.java:277)
at org.jboss.modules.ModuleClassLoader$1.loadClassLocal(ModuleClassLoader.java:92)
at org.jboss.modules.Module.loadModuleClass(Module.java:568)
at org.jboss.modules.ModuleClassLoader.findClass(ModuleClassLoader.java:205)
at org.jboss.modules.ConcurrentClassLoader.performLoadClassUnchecked(ConcurrentClassLoader.java:459)
at org.jboss.modules.ConcurrentClassLoader.performLoadClassChecked(ConcurrentClassLoader.java:447)
at org.jboss.modules.ConcurrentClassLoader.performLoadClassChecked(ConcurrentClassLoader.java:414)
at org.jboss.modules.ConcurrentClassLoader.performLoadClass(ConcurrentClassLoader.java:389)
at org.jboss.modules.ConcurrentClassLoader.loadClass(ConcurrentClassLoader.java:134)
at java.lang.Class.forName0(Native Method)
at java.lang.Class.forName(Class.java:247)
at org.jboss.modules.Module.run(Module.java:300)
at org.jboss.modules.Main.main(Main.java:460)