diff --git a/django/db/migrations/autodetector.py b/django/db/migrations/autodetector.py
index 04e651ec4a..0616ea4dbe 100644
--- a/django/db/migrations/autodetector.py
+++ b/django/db/migrations/autodetector.py
@@ -179,6 +179,7 @@ class MigrationAutodetector:
         self.generate_removed_indexes()
         # Generate field renaming operations.
         self.generate_renamed_fields()
+        self.generate_renamed_indexes()
         # Generate removal of foo together.
         self.generate_removed_altered_unique_together()
         self.generate_removed_altered_index_together()
@@ -1187,14 +1188,41 @@ class MigrationAutodetector:
 
             old_indexes = old_model_state.options[option_name]
             new_indexes = new_model_state.options[option_name]
-            add_idx = [idx for idx in new_indexes if idx not in old_indexes]
-            rem_idx = [idx for idx in old_indexes if idx not in new_indexes]
+            added_indexes = [idx for idx in new_indexes if idx not in old_indexes]
+            removed_indexes = [idx for idx in old_indexes if idx not in new_indexes]
+            renamed_indexes = []
+            # Find renamed indexes.
+            remove_from_added = []
+            remove_from_removed = []
+            for new_index in added_indexes:
+                new_index_dec = new_index.deconstruct()
+                new_index_name = new_index_dec[2].pop("name")
+                for old_index in removed_indexes:
+                    old_index_dec = old_index.deconstruct()
+                    old_index_name = old_index_dec[2].pop("name")
+                    # Indexes are the same except for the names.
+                    if (
+                        new_index_dec == old_index_dec
+                        and new_index_name != old_index_name
+                    ):
+                        renamed_indexes.append((old_index_name, new_index_name, None))
+                        remove_from_added.append(new_index)
+                        remove_from_removed.append(old_index)
+            # Remove renamed indexes from the lists of added and removed
+            # indexes.
+            added_indexes = [
+                idx for idx in added_indexes if idx not in remove_from_added
+            ]
+            removed_indexes = [
+                idx for idx in removed_indexes if idx not in remove_from_removed
+            ]
 
             self.altered_indexes.update(
                 {
                     (app_label, model_name): {
-                        "added_indexes": add_idx,
-                        "removed_indexes": rem_idx,
+                        "added_indexes": added_indexes,
+                        "removed_indexes": removed_indexes,
+                        "renamed_indexes": renamed_indexes,
                     }
                 }
             )
@@ -1221,6 +1249,21 @@ class MigrationAutodetector:
                     ),
                 )
 
+    def generate_renamed_indexes(self):
+        for (app_label, model_name), alt_indexes in self.altered_indexes.items():
+            for old_index_name, new_index_name, old_fields in alt_indexes[
+                "renamed_indexes"
+            ]:
+                self.add_operation(
+                    app_label,
+                    operations.RenameIndex(
+                        model_name=model_name,
+                        new_name=new_index_name,
+                        old_name=old_index_name,
+                        old_fields=old_fields,
+                    ),
+                )
+
     def create_altered_constraints(self):
         option_name = operations.AddConstraint.option_name
         for app_label, model_name in sorted(self.kept_model_keys):
diff --git a/docs/releases/4.1.txt b/docs/releases/4.1.txt
index dc95a653c3..7c9f1beca6 100644
--- a/docs/releases/4.1.txt
+++ b/docs/releases/4.1.txt
@@ -350,6 +350,11 @@ Migrations
   :attr:`Meta.indexes <django.db.models.Options.indexes>` or
   :attr:`~django.db.models.Options.index_together` options.
 
+* The migrations autodetector now generates
+  :class:`~django.db.migrations.operations.RenameIndex` operations instead of
+  ``RemoveIndex`` and ``AddIndex``, when renaming indexes defined in the
+  :attr:`Meta.indexes <django.db.models.Options.indexes>`.
+
 Models
 ~~~~~~
 
diff --git a/tests/migrations/test_autodetector.py b/tests/migrations/test_autodetector.py
index 0d7a44e42d..a28477e590 100644
--- a/tests/migrations/test_autodetector.py
+++ b/tests/migrations/test_autodetector.py
@@ -2565,6 +2565,39 @@ class AutodetectorTests(TestCase):
             changes, "otherapp", 0, 0, model_name="book", name="book_title_author_idx"
         )
 
+    def test_rename_indexes(self):
+        book_renamed_indexes = ModelState(
+            "otherapp",
+            "Book",
+            [
+                ("id", models.AutoField(primary_key=True)),
+                ("author", models.ForeignKey("testapp.Author", models.CASCADE)),
+                ("title", models.CharField(max_length=200)),
+            ],
+            {
+                "indexes": [
+                    models.Index(
+                        fields=["author", "title"], name="renamed_book_title_author_idx"
+                    )
+                ],
+            },
+        )
+        changes = self.get_changes(
+            [self.author_empty, self.book_indexes],
+            [self.author_empty, book_renamed_indexes],
+        )
+        self.assertNumberMigrations(changes, "otherapp", 1)
+        self.assertOperationTypes(changes, "otherapp", 0, ["RenameIndex"])
+        self.assertOperationAttributes(
+            changes,
+            "otherapp",
+            0,
+            0,
+            model_name="book",
+            new_name="renamed_book_title_author_idx",
+            old_name="book_title_author_idx",
+        )
+
     def test_order_fields_indexes(self):
         """Test change detection of reordering of fields in indexes."""
         changes = self.get_changes(