diff --git a/docs/source/command_line.rst b/docs/source/command_line.rst
index d4dfad6c28ad6..9f074ee6e5f5e 100644
--- a/docs/source/command_line.rst
+++ b/docs/source/command_line.rst
@@ -297,6 +297,21 @@ Here are some more useful flags:
 
 - ``--ignore-missing-imports`` suppresses error messages about imports
   that cannot be resolved (see :ref:`follow-imports` for some examples).
+  This doesn't suppress errors about missing names in successfully resolved
+  modules. For example, if one has the following files::
+
+    package/__init__.py
+    package/mod.py
+
+  Then mypy will generate the following errors with ``--ignore-missing-imports``:
+
+  .. code-block:: python
+
+     import package.unknown  # No error, ignored
+     x = package.unknown.func()  # OK
+
+     from package import unknown  # No error, ignored
+     from package.mod import NonExisting  # Error: Module has no attribute 'NonExisting'
 
 - ``--no-strict-optional`` disables strict checking of ``Optional[...]``
   types and ``None`` values. With this option, mypy doesn't
diff --git a/docs/source/config_file.rst b/docs/source/config_file.rst
index 82dd7961a4cc4..dcd152328693b 100644
--- a/docs/source/config_file.rst
+++ b/docs/source/config_file.rst
@@ -201,7 +201,7 @@ overridden by the pattern sections matching the module name.
   strict Optional checks. If False, mypy treats ``None`` as
   compatible with every type.
 
-  **Note::** This was False by default
+  **Note:** This was False by default
   in mypy versions earlier than 0.600.
 
 - ``disallow_any_unimported`` (Boolean, default false) disallows usage of types that come
diff --git a/mypy/semanal.py b/mypy/semanal.py
index 9249547d35939..058fc36221d7a 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -1329,15 +1329,34 @@ def add_submodules_to_parent_modules(self, id: str, module_public: bool) -> None
         while '.' in id:
             parent, child = id.rsplit('.', 1)
             parent_mod = self.modules.get(parent)
-            if parent_mod and child not in parent_mod.names:
+            if parent_mod and self.allow_patching(parent_mod, child):
                 child_mod = self.modules.get(id)
                 if child_mod:
                     sym = SymbolTableNode(MODULE_REF, child_mod,
                                           module_public=module_public,
                                           no_serialize=True)
-                    parent_mod.names[child] = sym
+                else:
+                    # Construct a dummy Var with Any type.
+                    any_type = AnyType(TypeOfAny.from_unimported_type,
+                                       missing_import_name=id)
+                    var = Var(child, any_type)
+                    var._fullname = child
+                    var.is_ready = True
+                    var.is_suppressed_import = True
+                    sym = SymbolTableNode(GDEF, var,
+                                          module_public=module_public,
+                                          no_serialize=True)
+                parent_mod.names[child] = sym
             id = parent
 
+    def allow_patching(self, parent_mod: MypyFile, child: str) -> bool:
+        if child not in parent_mod.names:
+            return True
+        node = parent_mod.names[child].node
+        if isinstance(node, Var) and node.is_suppressed_import:
+            return True
+        return False
+
     def add_module_symbol(self, id: str, as_id: str, module_public: bool,
                           context: Context, module_hidden: bool = False) -> None:
         if id in self.modules:
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index 3e28bd5e9c6ed..a9c6fa0e75236 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -2312,3 +2312,33 @@ def run() -> None:
 [out]
 tmp/p/b.py:4: error: Revealed type is 'builtins.int'
 tmp/p/__init__.py:3: error: Revealed type is 'builtins.int'
+
+[case testMissingSubmoduleImportedWithIgnoreMissingImports]
+# flags: --ignore-missing-imports
+import whatever.works
+import a.b
+x = whatever.works.f()
+y = a.b.f()
+[file a/__init__.py]
+# empty
+[out]
+
+[case testMissingSubmoduleImportedWithIgnoreMissingImportsStub]
+# flags: --ignore-missing-imports --follow-imports=skip
+import whatever.works
+import a.b
+x = whatever.works.f()
+y = a.b.f()
+[file a/__init__.pyi]
+# empty
+[out]
+
+[case testMissingSubmoduleImportedWithIgnoreMissingImportsNested]
+# flags: --ignore-missing-imports
+import a.b.c.d
+y = a.b.c.d.f()
+[file a/__init__.py]
+# empty
+[file a/b/__init__.py]
+# empty
+[out]
diff --git a/test-data/unit/fine-grained-modules.test b/test-data/unit/fine-grained-modules.test
index 3506c5636d586..1442a7807d4da 100644
--- a/test-data/unit/fine-grained-modules.test
+++ b/test-data/unit/fine-grained-modules.test
@@ -221,7 +221,6 @@ main:1: error: Cannot find module named 'p.a'
 ==
 main:1: error: Cannot find module named 'p.a'
 main:1: note: (Perhaps setting MYPYPATH or using the "--ignore-missing-imports" flag would help)
-main:2: error: Module has no attribute "a"
 ==
 main:2: error: Argument 1 to "f" has incompatible type "int"; expected "str"
 [builtins fixtures/module.pyi]
@@ -826,7 +825,6 @@ a.py:2: error: Too many arguments for "g"
 ==
 a.py:1: error: Cannot find module named 'm.x'
 a.py:1: note: (Perhaps setting MYPYPATH or using the "--ignore-missing-imports" flag would help)
-a.py:2: error: Module has no attribute "x"
 
 [case testDeletePackage1]
 import p.a
@@ -873,7 +871,6 @@ main:2: error: Argument 1 to "f" has incompatible type "int"; expected "str"
 ==
 main:1: error: Cannot find module named 'p.a'
 main:1: note: (Perhaps setting MYPYPATH or using the "--ignore-missing-imports" flag would help)
-main:2: error: Module has no attribute "a"
 ==
 main:1: error: Cannot find module named 'p'
 main:1: note: (Perhaps setting MYPYPATH or using the "--ignore-missing-imports" flag would help)