diff --git a/ChangeLog b/ChangeLog
index 40e05883b1..0bc7f85f6d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -223,6 +223,11 @@ Release date: TBA
   Closes #4434
   Closes #5370
 
+* Fix false positive ``super-init-not-called`` for classes that inherit their ``init`` from
+  a parent.
+
+  Closes #4941
+
 * ``encoding`` can now be supplied as a positional argument to calls that open
   files without triggering ``unspecified-encoding``.
 
diff --git a/doc/whatsnew/2.13.rst b/doc/whatsnew/2.13.rst
index a31078850a..c9204109ec 100644
--- a/doc/whatsnew/2.13.rst
+++ b/doc/whatsnew/2.13.rst
@@ -128,6 +128,11 @@ Other Changes
 
   Closes #5483
 
+* Fix false positive ``super-init-not-called`` for classes that inherit their ``init`` from
+  a parent.
+
+  Closes #4941
+
 * Fix ``unnecessary_dict_index_lookup`` false positive when deleting a dictionary's entry.
 
   Closes #4716
diff --git a/pylint/checkers/classes/class_checker.py b/pylint/checkers/classes/class_checker.py
index c39ecafe46..a33efb910c 100644
--- a/pylint/checkers/classes/class_checker.py
+++ b/pylint/checkers/classes/class_checker.py
@@ -52,7 +52,7 @@
 """Classes checker for Python code"""
 import collections
 from itertools import chain, zip_longest
-from typing import Dict, List, Pattern
+from typing import Dict, List, Pattern, Set
 
 import astroid
 from astroid import bases, nodes
@@ -1939,6 +1939,7 @@ def _check_init(self, node: nodes.FunctionDef, klass_node: nodes.ClassDef) -> No
             return
         to_call = _ancestors_to_call(klass_node)
         not_called_yet = dict(to_call)
+        parents_with_called_inits: Set[bases.UnboundMethod] = set()
         for stmt in node.nodes_of_class(nodes.Call):
             expr = stmt.func
             if not isinstance(expr, nodes.Attribute) or expr.attrname != "__init__":
@@ -1971,7 +1972,9 @@ def _check_init(self, node: nodes.FunctionDef, klass_node: nodes.ClassDef) -> No
                     if isinstance(klass, astroid.objects.Super):
                         return
                     try:
-                        del not_called_yet[klass]
+                        method = not_called_yet.pop(klass)
+                        # Record that the class' init has been called
+                        parents_with_called_inits.add(node_frame_class(method))
                     except KeyError:
                         if klass not in to_call:
                             self.add_message(
@@ -1980,6 +1983,11 @@ def _check_init(self, node: nodes.FunctionDef, klass_node: nodes.ClassDef) -> No
             except astroid.InferenceError:
                 continue
         for klass, method in not_called_yet.items():
+            # Check if the init of the class that defines this init has already
+            # been called.
+            if node_frame_class(method) in parents_with_called_inits:
+                return
+
             # Return if klass is protocol
             if klass.qname() in utils.TYPING_PROTOCOLS:
                 return
diff --git a/pylint/checkers/imports.py b/pylint/checkers/imports.py
index b0daf4bd6e..951504324d 100644
--- a/pylint/checkers/imports.py
+++ b/pylint/checkers/imports.py
@@ -427,9 +427,7 @@ class ImportsChecker(DeprecatedMixin, BaseChecker):
         ),
     )
 
-    def __init__(
-        self, linter: Optional["PyLinter"] = None
-    ):  # pylint: disable=super-init-not-called # See https://github.com/PyCQA/pylint/issues/4941
+    def __init__(self, linter: Optional["PyLinter"] = None) -> None:
         BaseChecker.__init__(self, linter)
         self.import_graph: collections.defaultdict = collections.defaultdict(set)
         self._imports_stack: List[Tuple[Any, Any]] = []
diff --git a/pylint/checkers/stdlib.py b/pylint/checkers/stdlib.py
index a203f2d07c..11c755ecfd 100644
--- a/pylint/checkers/stdlib.py
+++ b/pylint/checkers/stdlib.py
@@ -463,9 +463,7 @@ class StdlibChecker(DeprecatedMixin, BaseChecker):
         ),
     }
 
-    def __init__(
-        self, linter: Optional["PyLinter"] = None
-    ):  # pylint: disable=super-init-not-called # See https://github.com/PyCQA/pylint/issues/4941
+    def __init__(self, linter: Optional["PyLinter"] = None) -> None:
         BaseChecker.__init__(self, linter)
         self._deprecated_methods: Set[Any] = set()
         self._deprecated_methods.update(DEPRECATED_METHODS[0])
diff --git a/tests/functional/s/super/super_init_not_called.py b/tests/functional/s/super/super_init_not_called.py
index d2e9cffd87..c8e9f09d1e 100644
--- a/tests/functional/s/super/super_init_not_called.py
+++ b/tests/functional/s/super/super_init_not_called.py
@@ -1,5 +1,5 @@
 """Tests for super-init-not-called."""
-# pylint: disable=too-few-public-methods
+# pylint: disable=too-few-public-methods, missing-class-docstring
 
 import ctypes
 
@@ -20,3 +20,31 @@ class UninferableChild(UninferableParent):  # [undefined-variable]
 
     def __init__(self):
         ...
+
+
+# Tests for not calling the init of a parent that does not define one
+# but inherits it.
+class GrandParentWithInit:
+    def __init__(self):
+        print(self)
+
+
+class ParentWithoutInit(GrandParentWithInit):
+    pass
+
+
+class ChildOne(ParentWithoutInit, GrandParentWithInit):
+    """Since ParentWithoutInit calls GrandParentWithInit it doesn't need to be called."""
+
+    def __init__(self):
+        GrandParentWithInit.__init__(self)
+
+
+class ChildTwo(ParentWithoutInit):
+    def __init__(self):
+        ParentWithoutInit.__init__(self)
+
+
+class ChildThree(ParentWithoutInit):
+    def __init__(self):  # [super-init-not-called]
+        ...
diff --git a/tests/functional/s/super/super_init_not_called.txt b/tests/functional/s/super/super_init_not_called.txt
index b453d8a856..b6a220c69f 100644
--- a/tests/functional/s/super/super_init_not_called.txt
+++ b/tests/functional/s/super/super_init_not_called.txt
@@ -1 +1,2 @@
 undefined-variable:18:23:18:40:UninferableChild:Undefined variable 'UninferableParent':UNDEFINED
+super-init-not-called:49:4:50:11:ChildThree.__init__:__init__ method from base class 'ParentWithoutInit' is not called:INFERENCE