diff --git a/numpy/ma/core.py b/numpy/ma/core.py
index fe092f55249a..f142532dbee2 100644
--- a/numpy/ma/core.py
+++ b/numpy/ma/core.py
@@ -6309,6 +6309,18 @@ def copy(self, *args, **kwargs):
         # precedent for this with `np.bool_` scalars.
         return self
 
+    def __setattr__(self, attr, value):
+        if not self.__has_singleton():
+            # allow the singleton to be initialized
+            return super(MaskedConstant, self).__setattr__(attr, value)
+        elif self is self.__singleton:
+            raise AttributeError(
+                "attributes of {!r} are not writeable".format(self))
+        else:
+            # duplicate instance - we can end up here from __array_finalize__,
+            # where we set the __class__ attribute
+            return super(MaskedConstant, self).__setattr__(attr, value)
+
 
 masked = masked_singleton = MaskedConstant()
 masked_array = MaskedArray
diff --git a/numpy/ma/tests/test_core.py b/numpy/ma/tests/test_core.py
index d5622e4bb878..8c631d95d4da 100644
--- a/numpy/ma/tests/test_core.py
+++ b/numpy/ma/tests/test_core.py
@@ -4981,6 +4981,10 @@ class Sub(type(np.ma.masked)): pass
         assert_(a is not np.ma.masked)
         assert_not_equal(repr(a), 'masked')
 
+    def test_attributes_readonly(self):
+        assert_raises(AttributeError, setattr, np.ma.masked, 'shape', (1,))
+        assert_raises(AttributeError, setattr, np.ma.masked, 'dtype', np.int64)
+
 
 class TestMaskedWhereAliases(object):