diff --git a/pandas/core/series.py b/pandas/core/series.py
index ff780356104fa..6d818aa1684c4 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -235,6 +235,13 @@ def __init__(
                 copy = False
 
             elif isinstance(data, np.ndarray):
+                if len(data.dtype):
+                    # GH#13296 we are dealing with a compound dtype, which
+                    #  should be treated as 2D
+                    raise ValueError(
+                        "Cannot construct a Series from an ndarray with "
+                        "compound dtype.  Use DataFrame instead."
+                    )
                 pass
             elif isinstance(data, ABCSeries):
                 if name is None:
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index fffb9c577bf3d..20a83ec4cd162 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -67,6 +67,14 @@ def test_invalid_dtype(self):
             with pytest.raises(TypeError, match=msg):
                 Series([], name="time", dtype=dtype)
 
+    def test_invalid_compound_dtype(self):
+        # GH#13296
+        c_dtype = np.dtype([("a", "i8"), ("b", "f4")])
+        cdt_arr = np.array([(1, 0.4), (256, -13)], dtype=c_dtype)
+
+        with pytest.raises(ValueError, match="Use DataFrame instead"):
+            Series(cdt_arr, index=["A", "B"])
+
     def test_scalar_conversion(self):
 
         # Pass in scalar is disabled