diff --git a/packages/flutter/lib/src/material/app_bar.dart b/packages/flutter/lib/src/material/app_bar.dart
index 53705ebfb19..9cdc638d50d 100644
--- a/packages/flutter/lib/src/material/app_bar.dart
+++ b/packages/flutter/lib/src/material/app_bar.dart
@@ -763,7 +763,8 @@ class _AppBarState extends State<AppBar> {
   }
 
   void _handleScrollNotification(ScrollNotification notification) {
-    if (notification is ScrollUpdateNotification && widget.notificationPredicate(notification)) {
+    if (notification is ScrollUpdateNotification && widget.notificationPredicate(notification)
+      && Scaffold.isBodyDescendant(notification.context!)) {
       final bool oldScrolledUnder = _scrolledUnder;
       final ScrollMetrics metrics = notification.metrics;
       switch (metrics.axisDirection) {
diff --git a/packages/flutter/lib/src/material/scaffold.dart b/packages/flutter/lib/src/material/scaffold.dart
index 75a377012f4..b483212994f 100644
--- a/packages/flutter/lib/src/material/scaffold.dart
+++ b/packages/flutter/lib/src/material/scaffold.dart
@@ -1994,6 +1994,17 @@ class Scaffold extends StatefulWidget {
     }
   }
 
+  /// Whether the given context is descendant of the [Scaffold.body].
+  ///
+  /// This is used by [AppBar] to determine if the [AppBar] should listen to
+  /// [ScrollNotification] from the [Scrollable]s in the [Scaffold.body].
+  ///
+  /// It returns true if the given context is descendant of the [Scaffold.body].
+  static bool isBodyDescendant(BuildContext context) {
+    final _BodyBuilder? body = context.findAncestorWidgetOfExactType<_BodyBuilder>();
+    return body != null;
+  }
+
   @override
   ScaffoldState createState() => ScaffoldState();
 }
diff --git a/packages/flutter/test/material/app_bar_test.dart b/packages/flutter/test/material/app_bar_test.dart
index 8c43d4a0b8b..bff098e8159 100644
--- a/packages/flutter/test/material/app_bar_test.dart
+++ b/packages/flutter/test/material/app_bar_test.dart
@@ -4501,4 +4501,75 @@ void main() {
         expect(buttonWasPressed, isFalse);
     });
   });
+
+  testWidgets("scrolledUnderElevation only listens to scroll notifications from Scaffold's body", (WidgetTester tester) async {
+    final GlobalKey<ScaffoldState> scaffoldKey = GlobalKey<ScaffoldState>();
+    Widget buildWidget() {
+      return MaterialApp(
+        theme: ThemeData(useMaterial3: true),
+        home: Scaffold(
+          key: scaffoldKey,
+          appBar: AppBar(),
+          drawer: Drawer(
+            child: ListView.builder(
+              itemCount: 10,
+              itemBuilder: (BuildContext context, int index) {
+                return ListTile(
+                  title: Text('$index'),
+                );
+              }
+            ),
+          ),
+          body: ListView.builder(
+            itemCount: 10,
+            itemBuilder: (BuildContext context, int index) {
+              return ListTile(
+                title: Text('$index'),
+              );
+            }
+          ),
+        ),
+      );
+    }
+
+    await tester.pumpWidget(buildWidget());
+
+    // The first Material is the AppBar's Material.
+    Material getMaterial() => tester.widget<Material>(find.descendant(
+      of: find.byType(AppBar),
+      matching: find.byType(Material),
+    ).first);
+
+    expect(getMaterial().elevation, 0.0);
+
+    // Scroll down the list view in the body.
+    await tester.drag(find.byType(ListView), const Offset(0.0, -300.0));
+    await tester.pumpAndSettle();
+
+    // AppBar should be elevated.
+    expect(getMaterial().elevation, 3.0);
+
+    // Scroll up the list view in the body.
+    await tester.drag(find.byType(ListView), const Offset(0.0, 300.0));
+    await tester.pumpAndSettle();
+
+    // AppBar should not be elevated.
+    expect(getMaterial().elevation, 0.0);
+
+    final ScaffoldState state = tester.firstState(find.byType(Scaffold));
+
+    // Open the drawer.
+    state.openDrawer();
+    await tester.pump();
+    await tester.pump(const Duration(seconds: 1));
+
+    expect(scaffoldKey.currentState!.isDrawerOpen, isTrue);
+
+    // Scroll down the list view in the drawer.
+    await tester.drag(find.byType(ListView).last, const Offset(0.0, -250.0));
+    await tester.pump();
+
+    // AppBar should still not be elevated.
+    expect(getMaterial().elevation, 0.0);
+  });
 }
diff --git a/packages/flutter/test/material/scaffold_test.dart b/packages/flutter/test/material/scaffold_test.dart
index 3f040b1f658..c2bac885212 100644
--- a/packages/flutter/test/material/scaffold_test.dart
+++ b/packages/flutter/test/material/scaffold_test.dart
@@ -2698,6 +2698,22 @@ void main() {
 
     expect(tester.takeException(), isNull);
   });
+
+  testWidgets('Scaffold.isBodyDescendant checks if given context is descendant of the body', (WidgetTester tester) async {
+    final GlobalKey scaffoldKey = GlobalKey();
+    final GlobalKey bodyChildKey = GlobalKey();
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Scaffold(
+          key: scaffoldKey,
+          body: SizedBox(key: bodyChildKey),
+        ),
+      ),
+    );
+
+    expect(Scaffold.isBodyDescendant(scaffoldKey.currentContext!), false);
+    expect(Scaffold.isBodyDescendant(bodyChildKey.currentContext!), true);
+  });
 }
 
 class _GeometryListener extends StatefulWidget {