diff --git a/src/material/sidenav/BUILD.bazel b/src/material/sidenav/BUILD.bazel
index 52b318181a63..29327a427d67 100644
--- a/src/material/sidenav/BUILD.bazel
+++ b/src/material/sidenav/BUILD.bazel
@@ -24,6 +24,7 @@ ng_module(
         "//src/cdk/bidi",
         "//src/cdk/coercion",
         "//src/cdk/keycodes",
+        "//src/cdk/overlay",
         "//src/cdk/scrolling",
         "//src/material/core",
         "@npm//@angular/core",
@@ -57,6 +58,7 @@ ng_test_library(
         "//src/cdk/a11y",
         "//src/cdk/bidi",
         "//src/cdk/keycodes",
+        "//src/cdk/overlay",
         "//src/cdk/platform",
         "//src/cdk/scrolling",
         "//src/cdk/testing",
diff --git a/src/material/sidenav/drawer.spec.ts b/src/material/sidenav/drawer.spec.ts
index 7e21171f5b97..7fd58b067661 100644
--- a/src/material/sidenav/drawer.spec.ts
+++ b/src/material/sidenav/drawer.spec.ts
@@ -2,6 +2,7 @@ import {A11yModule} from '@angular/cdk/a11y';
 import {Direction} from '@angular/cdk/bidi';
 import {ESCAPE} from '@angular/cdk/keycodes';
 import {CdkScrollable} from '@angular/cdk/scrolling';
+import {OverlayKeyboardDispatcher, OverlayRef} from '@angular/cdk/overlay';
 import {
   createKeyboardEvent,
   dispatchEvent,
@@ -22,7 +23,13 @@ import {NoopAnimationsModule} from '@angular/platform-browser/animations';
 import {MatDrawer, MatDrawerContainer, MatSidenavModule} from './index';
 
 describe('MatDrawer', () => {
+  let fakeKeyboardDispatcher: OverlayKeyboardDispatcher;
+
   beforeEach(waitForAsync(() => {
+    fakeKeyboardDispatcher = {
+      _attachedOverlays: [] as OverlayRef[],
+    } as OverlayKeyboardDispatcher;
+
     TestBed.configureTestingModule({
       imports: [
         MatSidenavModule,
@@ -39,6 +46,12 @@ describe('MatDrawer', () => {
         IndirectDescendantDrawer,
         NestedDrawerContainers,
       ],
+      providers: [
+        {
+          provide: OverlayKeyboardDispatcher,
+          useValue: fakeKeyboardDispatcher,
+        },
+      ],
     });
   }));
 
@@ -237,6 +250,33 @@ describe('MatDrawer', () => {
       expect(event.defaultPrevented).toBe(false);
     }));
 
+    it('should not close when pressing escape while an overlay is open', fakeAsync(() => {
+      const fixture = TestBed.createComponent(BasicTestApp);
+      fixture.detectChanges();
+
+      const testComponent: BasicTestApp = fixture.debugElement.componentInstance;
+      const drawer = fixture.debugElement.query(By.directive(MatDrawer))!;
+
+      drawer.componentInstance.open();
+      fixture.detectChanges();
+      tick();
+
+      expect(testComponent.closeCount).withContext('Expected no close events.').toBe(0);
+      expect(testComponent.closeStartCount).withContext('Expected no close start events.').toBe(0);
+
+      fakeKeyboardDispatcher._attachedOverlays.push(null!);
+      const event = createKeyboardEvent('keydown', ESCAPE);
+      dispatchEvent(drawer.nativeElement, event);
+      fixture.detectChanges();
+      flush();
+
+      expect(testComponent.closeCount).withContext('Expected still no close events.').toBe(0);
+      expect(testComponent.closeStartCount)
+        .withContext('Expected still no close start events.')
+        .toBe(0);
+      expect(event.defaultPrevented).toBe(false);
+    }));
+
     it('should fire the open event when open on init', fakeAsync(() => {
       const fixture = TestBed.createComponent(DrawerSetToOpenedTrue);
 
diff --git a/src/material/sidenav/drawer.ts b/src/material/sidenav/drawer.ts
index efbb55507e75..1e51ce3c00dd 100644
--- a/src/material/sidenav/drawer.ts
+++ b/src/material/sidenav/drawer.ts
@@ -16,6 +16,7 @@ import {Directionality} from '@angular/cdk/bidi';
 import {BooleanInput, coerceBooleanProperty} from '@angular/cdk/coercion';
 import {ESCAPE, hasModifierKey} from '@angular/cdk/keycodes';
 import {Platform} from '@angular/cdk/platform';
+import {OverlayKeyboardDispatcher} from '@angular/cdk/overlay';
 import {CdkScrollable, ScrollDispatcher, ViewportRuler} from '@angular/cdk/scrolling';
 import {DOCUMENT} from '@angular/common';
 import {
@@ -179,6 +180,7 @@ export class MatDrawer implements AfterViewInit, OnDestroy {
   private _renderer = inject(Renderer2);
   private readonly _interactivityChecker = inject(InteractivityChecker);
   private _doc = inject(DOCUMENT, {optional: true})!;
+  private _keyboardDispatcher = inject(OverlayKeyboardDispatcher, {optional: true});
   _container? = inject<MatDrawerContainer>(MAT_DRAWER_CONTAINER, {optional: true});
 
   private _focusTrap: FocusTrap | null = null;
@@ -360,19 +362,22 @@ export class MatDrawer implements AfterViewInit, OnDestroy {
     this._ngZone.runOutsideAngular(() => {
       const element = this._elementRef.nativeElement;
       (fromEvent(element, 'keydown') as Observable<KeyboardEvent>)
-        .pipe(
-          filter(event => {
-            return event.keyCode === ESCAPE && !this.disableClose && !hasModifierKey(event);
-          }),
-          takeUntil(this._destroyed),
-        )
-        .subscribe(event =>
-          this._ngZone.run(() => {
-            this.close();
-            event.stopPropagation();
-            event.preventDefault();
-          }),
-        );
+        .pipe(takeUntil(this._destroyed))
+        .subscribe(event => {
+          // Skip keyboard events if there are open overlays since they may be
+          // placed inside the sidenav and cause it to close unexpectedly.
+          if (this._keyboardDispatcher && this._keyboardDispatcher._attachedOverlays.length > 0) {
+            return;
+          }
+
+          if (event.keyCode === ESCAPE && !this.disableClose && !hasModifierKey(event)) {
+            this._ngZone.run(() => {
+              this.close();
+              event.stopPropagation();
+              event.preventDefault();
+            });
+          }
+        });
 
       this._eventCleanups = [
         this._renderer.listen(element, 'transitionrun', this._handleTransitionEvent),