diff --git a/src/material/menu/menu-panel.ts b/src/material/menu/menu-panel.ts
index a5f0f1732a46..53b2b0094a81 100644
--- a/src/material/menu/menu-panel.ts
+++ b/src/material/menu/menu-panel.ts
@@ -33,6 +33,7 @@ export interface MatMenuPanel<T = any> {
   focusFirstItem: (origin?: FocusOrigin) => void;
   resetActiveItem: () => void;
   setPositionClasses?: (x: MenuPositionX, y: MenuPositionY) => void;
+  openedBy?: EventEmitter<any>;
   setElevation?(depth: number): void;
   lazyContent?: MatMenuContent;
   backdropClass?: string;
diff --git a/src/material/menu/menu-trigger.ts b/src/material/menu/menu-trigger.ts
index 75c0d1afd643..e7e356172012 100644
--- a/src/material/menu/menu-trigger.ts
+++ b/src/material/menu/menu-trigger.ts
@@ -35,7 +35,7 @@ import {
   isDevMode,
 } from '@angular/core';
 import {normalizePassiveListenerOptions} from '@angular/cdk/platform';
-import {asapScheduler, merge, of as observableOf, Subscription} from 'rxjs';
+import {asapScheduler, merge, of as observableOf, Subscription, Subject} from 'rxjs';
 import {delay, filter, take, takeUntil} from 'rxjs/operators';
 import {MatMenu} from './menu';
 import {throwMatMenuMissingError, throwMatMenuRecursiveError} from './menu-errors';
@@ -87,7 +87,7 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
   private _menuOpen: boolean = false;
   private _closingActionsSubscription = Subscription.EMPTY;
   private _hoverSubscription = Subscription.EMPTY;
-  private _menuCloseSubscription = Subscription.EMPTY;
+  private _menuChanged = new Subject<void>();
   private _scrollStrategy: () => ScrollStrategy;
 
   /**
@@ -119,14 +119,22 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
     }
 
     this._menu = menu;
-    this._menuCloseSubscription.unsubscribe();
+    this._menuChanged.next();
 
     if (menu) {
       if (isDevMode() && menu === this._parentMenu) {
         throwMatMenuRecursiveError();
       }
 
-      this._menuCloseSubscription = menu.close.asObservable().subscribe(reason => {
+      if (menu.openedBy) {
+        menu.openedBy.pipe(takeUntil(this._menuChanged)).subscribe((reason?: MatMenuTrigger) => {
+          if (reason && reason !== this) {
+            this._destroyMenu();
+          }
+        });
+      }
+
+      menu.close.pipe(takeUntil(this._menuChanged)).subscribe(reason => {
         this._destroyMenu();
 
         // If a click closed the menu, we should close the entire chain of nested menus.
@@ -209,9 +217,9 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
     this._element.nativeElement.removeEventListener('touchstart', this._handleTouchStart,
         passiveEventListenerOptions);
 
-    this._menuCloseSubscription.unsubscribe();
     this._closingActionsSubscription.unsubscribe();
     this._hoverSubscription.unsubscribe();
+    this._menuChanged.complete();
   }
 
   /** Whether the menu is open. */
@@ -324,11 +332,16 @@ export class MatMenuTrigger implements AfterContentInit, OnDestroy {
    * the menu was opened via the keyboard.
    */
   private _initMenu(): void {
-    this.menu.parentMenu = this.triggersSubmenu() ? this._parentMenu : undefined;
-    this.menu.direction = this.dir;
+    const menu = this.menu;
+    menu.parentMenu = this.triggersSubmenu() ? this._parentMenu : undefined;
+    menu.direction = this.dir;
     this._setMenuElevation();
     this._setIsMenuOpen(true);
-    this.menu.focusFirstItem(this._openedBy || 'program');
+    menu.focusFirstItem(this._openedBy || 'program');
+
+    if (menu.openedBy) {
+      menu.openedBy.emit(this);
+    }
   }
 
   /** Updates the menu elevation based on the amount of parent menus that it has. */
diff --git a/src/material/menu/menu.spec.ts b/src/material/menu/menu.spec.ts
index 24a5d5c5224c..b78de87f8fb0 100644
--- a/src/material/menu/menu.spec.ts
+++ b/src/material/menu/menu.spec.ts
@@ -905,6 +905,22 @@ describe('MatMenu', () => {
     expect(document.activeElement).toBe(overlayContainerElement.querySelector('.mat-menu-panel'));
   }));
 
+  it('should close the menu if it is opened by a different trigger', fakeAsync(() => {
+    const fixture = createComponent(MenuWithMultipleTriggers);
+    fixture.detectChanges();
+
+    fixture.componentInstance.triggers.first.openMenu();
+    fixture.detectChanges();
+    flush();
+    expect(overlayContainerElement.querySelectorAll('.mat-menu-panel').length).toBe(1);
+
+    fixture.componentInstance.triggers.last.openMenu();
+    fixture.detectChanges();
+    flush();
+    expect(overlayContainerElement.querySelectorAll('.mat-menu-panel').length).toBe(1);
+
+  }));
+
   describe('lazy rendering', () => {
     it('should be able to render the menu content lazily', fakeAsync(() => {
       const fixture = createComponent(SimpleLazyMenu);
@@ -2640,3 +2656,17 @@ class LazyMenuWithOnPush {
 })
 class InvalidRecursiveMenu {
 }
+
+@Component({
+  template: `
+    <button [matMenuTriggerFor]="menu">First trigger</button>
+    <button [matMenuTriggerFor]="menu">Second trigger</button>
+    <mat-menu #menu="matMenu">
+      <button mat-menu-item>Item one</button>
+      <button mat-menu-item>Item two</button>
+    </mat-menu>
+  `
+})
+class MenuWithMultipleTriggers {
+  @ViewChildren(MatMenuTrigger) triggers: QueryList<MatMenuTrigger>;
+}
diff --git a/src/material/menu/menu.ts b/src/material/menu/menu.ts
index 81dc31059707..943dad39dca4 100644
--- a/src/material/menu/menu.ts
+++ b/src/material/menu/menu.ts
@@ -245,6 +245,13 @@ export class _MatMenuBase implements AfterContentInit, MatMenuPanel<MatMenuItem>
   @Output() readonly closed: EventEmitter<void | 'click' | 'keydown' | 'tab'> =
       new EventEmitter<void | 'click' | 'keydown' | 'tab'>();
 
+
+  /**
+   * Stream that emits the trigger that the menu was opened by.
+   * @docs-private
+   */
+  @Output() openedBy = new EventEmitter<any>();
+
   /**
    * Event emitted when the menu is closed.
    * @deprecated Switch to `closed` instead
@@ -281,6 +288,7 @@ export class _MatMenuBase implements AfterContentInit, MatMenuPanel<MatMenuItem>
     this._directDescendantItems.destroy();
     this._tabSubscription.unsubscribe();
     this.closed.complete();
+    this.openedBy.complete();
   }
 
   /** Stream that emits whenever the hovered menu item changes. */
diff --git a/tools/public_api_guard/material/menu.d.ts b/tools/public_api_guard/material/menu.d.ts
index 24a5cf0c1e97..6bf34f1e8f6e 100644
--- a/tools/public_api_guard/material/menu.d.ts
+++ b/tools/public_api_guard/material/menu.d.ts
@@ -25,6 +25,7 @@ export declare class _MatMenuBase implements AfterContentInit, MatMenuPanel<MatM
     set hasBackdrop(value: boolean | undefined);
     items: QueryList<MatMenuItem>;
     lazyContent: MatMenuContent;
+    openedBy: EventEmitter<any>;
     get overlapTrigger(): boolean;
     set overlapTrigger(value: boolean);
     overlayPanelClass: string | string[];
@@ -54,7 +55,7 @@ export declare class _MatMenuBase implements AfterContentInit, MatMenuPanel<MatM
     setPositionClasses(posX?: MenuPositionX, posY?: MenuPositionY): void;
     static ngAcceptInputType_hasBackdrop: BooleanInput;
     static ngAcceptInputType_overlapTrigger: BooleanInput;
-    static ɵdir: i0.ɵɵDirectiveDefWithMeta<_MatMenuBase, never, never, { "backdropClass": "backdropClass"; "ariaLabel": "aria-label"; "ariaLabelledby": "aria-labelledby"; "ariaDescribedby": "aria-describedby"; "xPosition": "xPosition"; "yPosition": "yPosition"; "overlapTrigger": "overlapTrigger"; "hasBackdrop": "hasBackdrop"; "panelClass": "class"; "classList": "classList"; }, { "closed": "closed"; "close": "close"; }, ["lazyContent", "_allItems", "items"]>;
+    static ɵdir: i0.ɵɵDirectiveDefWithMeta<_MatMenuBase, never, never, { "backdropClass": "backdropClass"; "ariaLabel": "aria-label"; "ariaLabelledby": "aria-labelledby"; "ariaDescribedby": "aria-describedby"; "xPosition": "xPosition"; "yPosition": "yPosition"; "overlapTrigger": "overlapTrigger"; "hasBackdrop": "hasBackdrop"; "panelClass": "class"; "classList": "classList"; }, { "closed": "closed"; "openedBy": "openedBy"; "close": "close"; }, ["lazyContent", "_allItems", "items"]>;
     static ɵfac: i0.ɵɵFactoryDef<_MatMenuBase, never>;
 }
 
@@ -137,6 +138,7 @@ export interface MatMenuPanel<T = any> {
     focusFirstItem: (origin?: FocusOrigin) => void;
     hasBackdrop?: boolean;
     lazyContent?: MatMenuContent;
+    openedBy?: EventEmitter<any>;
     overlapTrigger: boolean;
     overlayPanelClass?: string | string[];
     readonly panelId?: string;