diff --git a/src/material/tooltip/tooltip.spec.ts b/src/material/tooltip/tooltip.spec.ts
index 06f887ef99ca..75bc71db1a3c 100644
--- a/src/material/tooltip/tooltip.spec.ts
+++ b/src/material/tooltip/tooltip.spec.ts
@@ -63,6 +63,7 @@ describe('MatTooltip', () => {
         DynamicTooltipsDemo,
         TooltipOnTextFields,
         TooltipOnDraggableElement,
+        DataBoundAriaLabelTooltip,
       ],
       providers: [
         {provide: Platform, useFactory: () => platform},
@@ -441,20 +442,31 @@ describe('MatTooltip', () => {
       expect(overlayContainerElement.textContent).toBe('');
     }));
 
-    it('should have an aria-described element with the tooltip message', () => {
+    it('should have an aria-described element with the tooltip message', fakeAsync(() => {
       const dynamicTooltipsDemoFixture = TestBed.createComponent(DynamicTooltipsDemo);
       const dynamicTooltipsComponent = dynamicTooltipsDemoFixture.componentInstance;
 
       dynamicTooltipsComponent.tooltips = ['Tooltip One', 'Tooltip Two'];
       dynamicTooltipsDemoFixture.detectChanges();
+      tick();
 
-      const buttons = dynamicTooltipsComponent.getButtons();
+      const buttons = dynamicTooltipsDemoFixture.nativeElement.querySelectorAll('button');
       const firstButtonAria = buttons[0].getAttribute('aria-describedby');
       expect(document.querySelector(`#${firstButtonAria}`)!.textContent).toBe('Tooltip One');
 
       const secondButtonAria = buttons[1].getAttribute('aria-describedby');
       expect(document.querySelector(`#${secondButtonAria}`)!.textContent).toBe('Tooltip Two');
-    });
+    }));
+
+    it('should not add an ARIA description for elements that have the same text as a' +
+      'data-bound aria-label', fakeAsync(() => {
+        const ariaLabelFixture = TestBed.createComponent(DataBoundAriaLabelTooltip);
+        ariaLabelFixture.detectChanges();
+        tick();
+
+        const button = ariaLabelFixture.nativeElement.querySelector('button');
+        expect(button.getAttribute('aria-describedby')).toBeFalsy();
+      }));
 
     it('should not try to dispose the tooltip when destroyed and done hiding', fakeAsync(() => {
       tooltipDirective.show();
@@ -1011,14 +1023,16 @@ class OnPushTooltipDemo {
 })
 class DynamicTooltipsDemo {
   tooltips: Array<string> = [];
+}
 
-  constructor(private _elementRef: ElementRef<HTMLElement>) {}
-
-  getButtons() {
-    return this._elementRef.nativeElement.querySelectorAll('button');
-  }
+@Component({
+  template: `<button [matTooltip]="message" [attr.aria-label]="message">Click me</button>`,
+})
+class DataBoundAriaLabelTooltip {
+  message = 'Hello there';
 }
 
+
 @Component({
   template: `
     <input
diff --git a/src/material/tooltip/tooltip.ts b/src/material/tooltip/tooltip.ts
index 040cdaf2d233..803efc4ec663 100644
--- a/src/material/tooltip/tooltip.ts
+++ b/src/material/tooltip/tooltip.ts
@@ -180,7 +180,15 @@ export class MatTooltip implements OnDestroy, OnInit {
       this.hide(0);
     } else {
       this._updateTooltipMessage();
-      this._ariaDescriber.describe(this._elementRef.nativeElement, this.message);
+      this._ngZone.runOutsideAngular(() => {
+        // The `AriaDescriber` has some functionality that avoids adding a description if it's the
+        // same as the `aria-label` of an element, however we can't know whether the tooltip trigger
+        // has a data-bound `aria-label` or when it'll be set for the first time. We can avoid the
+        // issue by deferring the description by a tick so Angular has time to set the `aria-label`.
+        Promise.resolve().then(() => {
+          this._ariaDescriber.describe(this._elementRef.nativeElement, this.message);
+        });
+      });
     }
   }