diff --git a/CHANGES b/CHANGES
index c72929a19..cd0e55aff 100644
--- a/CHANGES
+++ b/CHANGES
@@ -45,6 +45,7 @@ Bugs fixed
 * #6961: latex: warning for babel shown twice
 * #6559: Wrong node-ids are generated in glossary directive
 * #6986: apidoc: misdetects module name for .so file inside module
+* #6999: napoleon: fails to parse tilde in :exc: role
 
 Testing
 --------
diff --git a/sphinx/ext/napoleon/docstring.py b/sphinx/ext/napoleon/docstring.py
index a06a79cea..81f2496cb 100644
--- a/sphinx/ext/napoleon/docstring.py
+++ b/sphinx/ext/napoleon/docstring.py
@@ -101,8 +101,8 @@ class GoogleDocstring:
 
     """
 
-    _name_rgx = re.compile(r"^\s*((?::(?P<role>\S+):)?`(?P<name>[a-zA-Z0-9_.-]+)`|"
-                           r" (?P<name2>[a-zA-Z0-9_.-]+))\s*", re.X)
+    _name_rgx = re.compile(r"^\s*((?::(?P<role>\S+):)?`(?P<name>~?[a-zA-Z0-9_.-]+)`|"
+                           r" (?P<name2>~?[a-zA-Z0-9_.-]+))\s*", re.X)
 
     def __init__(self, docstring: Union[str, List[str]], config: SphinxConfig = None,
                  app: Sphinx = None, what: str = '', name: str = '',
diff --git a/tests/test_ext_napoleon_docstring.py b/tests/test_ext_napoleon_docstring.py
index 9547a9d2b..2ce754eff 100644
--- a/tests/test_ext_napoleon_docstring.py
+++ b/tests/test_ext_napoleon_docstring.py
@@ -479,6 +479,8 @@ Raises:
         If the dimensions couldn't be parsed.
     `InvalidArgumentsError`
         If the arguments are invalid.
+    :exc:`~ValueError`
+        If the arguments are wrong.
 
 """, """
 Example Function
@@ -488,6 +490,7 @@ Example Function
 :raises AttributeError: errors for missing attributes.
 :raises ~InvalidDimensionsError: If the dimensions couldn't be parsed.
 :raises InvalidArgumentsError: If the arguments are invalid.
+:raises ~ValueError: If the arguments are wrong.
 """),
                       ################################
                       ("""