diff --git a/sklearn/linear_model/_glm/glm.py b/sklearn/linear_model/_glm/glm.py
index 8974b16919aaa..81c85f41bfeac 100644
--- a/sklearn/linear_model/_glm/glm.py
+++ b/sklearn/linear_model/_glm/glm.py
@@ -424,7 +424,11 @@ def _get_loss(self):
     )
     @property
     def family(self):
-        """Ensure backward compatibility for the time of deprecation."""
+        """Ensure backward compatibility for the time of deprecation.
+
+        .. deprecated:: 1.1
+            Will be removed in 1.3
+        """
         if isinstance(self, PoissonRegressor):
             return "poisson"
         elif isinstance(self, GammaRegressor):
diff --git a/sklearn/tests/test_docstrings.py b/sklearn/tests/test_docstrings.py
index 7a470422ba961..f48eb6766c887 100644
--- a/sklearn/tests/test_docstrings.py
+++ b/sklearn/tests/test_docstrings.py
@@ -71,7 +71,13 @@ def filter_errors(errors, method, Klass=None):
 
         # Ignore PR02: Unknown parameters for properties. We sometimes use
         # properties for ducktyping, i.e. SGDClassifier.predict_proba
-        if code == "PR02" and Klass is not None and method is not None:
+        # Ignore GL08: Parsing of the method signature failed, possibly because this is
+        # a property. Properties are sometimes used for deprecated attributes and the
+        # attribute is already documented in the class docstring.
+        #
+        # All error codes:
+        # https://numpydoc.readthedocs.io/en/latest/validation.html#built-in-validation-checks
+        if code in ("PR02", "GL08") and Klass is not None and method is not None:
             method_obj = getattr(Klass, method)
             if isinstance(method_obj, property):
                 continue
diff --git a/sklearn/utils/deprecation.py b/sklearn/utils/deprecation.py
index 2ee07154dc49b..19d41aa1eaf85 100644
--- a/sklearn/utils/deprecation.py
+++ b/sklearn/utils/deprecation.py
@@ -70,7 +70,6 @@ def wrapped(*args, **kwargs):
         cls.__init__ = wrapped
 
         wrapped.__name__ = "__init__"
-        wrapped.__doc__ = self._update_doc(init.__doc__)
         wrapped.deprecated_original = init
 
         return cls
@@ -87,7 +86,6 @@ def wrapped(*args, **kwargs):
             warnings.warn(msg, category=FutureWarning)
             return fun(*args, **kwargs)
 
-        wrapped.__doc__ = self._update_doc(wrapped.__doc__)
         # Add a reference to the wrapped function so that we can introspect
         # on function arguments in Python 2 (already works in Python 3)
         wrapped.__wrapped__ = fun
@@ -103,18 +101,8 @@ def wrapped(*args, **kwargs):
             warnings.warn(msg, category=FutureWarning)
             return prop.fget(*args, **kwargs)
 
-        wrapped.__doc__ = self._update_doc(wrapped.__doc__)
-
         return wrapped
 
-    def _update_doc(self, olddoc):
-        newdoc = "DEPRECATED"
-        if self.extra:
-            newdoc = "%s: %s" % (newdoc, self.extra)
-        if olddoc:
-            newdoc = "%s\n\n    %s" % (newdoc, olddoc)
-        return newdoc
-
 
 def _is_deprecated(func):
     """Helper to check if func is wrapped by our deprecated decorator"""
diff --git a/sklearn/utils/tests/test_deprecation.py b/sklearn/utils/tests/test_deprecation.py
index e39486cc0318a..b810cfb85d3f6 100644
--- a/sklearn/utils/tests/test_deprecation.py
+++ b/sklearn/utils/tests/test_deprecation.py
@@ -65,12 +65,3 @@ def test_is_deprecated():
 
 def test_pickle():
     pickle.loads(pickle.dumps(mock_function))
-
-
-def test_deprecated_property_docstring_exists():
-    """Deprecated property contains the original docstring."""
-    mock_class_property = getattr(MockClass2, "n_features_")
-    assert (
-        "DEPRECATED: n_features_ is deprecated\n\n    Number of input features."
-        == mock_class_property.__doc__
-    )