diff --git a/src/cdk/stepper/stepper.ts b/src/cdk/stepper/stepper.ts
index d73622aab0c..c216a9556b2 100644
--- a/src/cdk/stepper/stepper.ts
+++ b/src/cdk/stepper/stepper.ts
@@ -84,9 +84,18 @@ export class CdkStep implements OnChanges {
   /** Whether user has seen the expanded step content or not. */
   interacted = false;
 
-  /** Label of the step. */
+  /** Plain text label of the step. */
   @Input() label: string;
 
+  /** Aria label for the tab. */
+  @Input('aria-label') ariaLabel: string;
+
+  /**
+   * Reference to the element that the tab is labelled by.
+   * Will be cleared if `aria-label` is set at the same time.
+   */
+  @Input('aria-labelledby') ariaLabelledby: string;
+
   /** Whether the user can return to this step once it has been marked as complted. */
   @Input()
   get editable(): boolean { return this._editable; }
diff --git a/src/lib/stepper/stepper-horizontal.html b/src/lib/stepper/stepper-horizontal.html
index e3e5b27458c..82947eebff7 100644
--- a/src/lib/stepper/stepper-horizontal.html
+++ b/src/lib/stepper/stepper-horizontal.html
@@ -9,6 +9,8 @@
                      [attr.aria-setsize]="_steps.length"
                      [attr.aria-controls]="_getStepContentId(i)"
                      [attr.aria-selected]="selectedIndex == i"
+                     [attr.aria-label]="step.ariaLabel || null"
+                     [attr.aria-labelledby]="(!step.ariaLabel && step.ariaLabelledby) ? step.ariaLabelledby : null"
                      [index]="i"
                      [state]="_getIndicatorType(i)"
                      [label]="step.stepLabel || step.label"
diff --git a/src/lib/stepper/stepper-vertical.html b/src/lib/stepper/stepper-vertical.html
index 95c1941d424..5ff402fa1e0 100644
--- a/src/lib/stepper/stepper-vertical.html
+++ b/src/lib/stepper/stepper-vertical.html
@@ -8,6 +8,8 @@
                    [attr.aria-setsize]="_steps.length"
                    [attr.aria-controls]="_getStepContentId(i)"
                    [attr.aria-selected]="selectedIndex === i"
+                   [attr.aria-label]="step.ariaLabel || null"
+                   [attr.aria-labelledby]="(!step.ariaLabel && step.ariaLabelledby) ? step.ariaLabelledby : null"
                    [index]="i"
                    [state]="_getIndicatorType(i)"
                    [label]="step.stepLabel || step.label"
diff --git a/src/lib/stepper/stepper.spec.ts b/src/lib/stepper/stepper.spec.ts
index 961eff34282..3cb330ed073 100644
--- a/src/lib/stepper/stepper.spec.ts
+++ b/src/lib/stepper/stepper.spec.ts
@@ -54,6 +54,7 @@ describe('MatStepper', () => {
         SimpleStepperWithStepControlAndCompletedBinding,
         SimpleMatHorizontalStepperApp,
         LinearStepperWithValidOptionalStep,
+        StepperWithAriaInputs,
       ],
       providers: [
         {provide: Directionality, useFactory: () => dir}
@@ -836,6 +837,46 @@ describe('MatStepper', () => {
       expect(stepper.selectedIndex).toBe(2);
     });
   });
+
+  describe('aria labelling', () => {
+    let fixture: ComponentFixture<StepperWithAriaInputs>;
+    let stepHeader: HTMLElement;
+
+    beforeEach(() => {
+      fixture = TestBed.createComponent(StepperWithAriaInputs);
+      fixture.detectChanges();
+      stepHeader = fixture.nativeElement.querySelector('.mat-step-header');
+    });
+
+    it('should not set aria-label or aria-labelledby attributes if they are not passed in', () => {
+      expect(stepHeader.hasAttribute('aria-label')).toBe(false);
+      expect(stepHeader.hasAttribute('aria-labelledby')).toBe(false);
+    });
+
+    it('should set the aria-label attribute', () => {
+      fixture.componentInstance.ariaLabel = 'First step';
+      fixture.detectChanges();
+
+      expect(stepHeader.getAttribute('aria-label')).toBe('First step');
+    });
+
+    it('should set the aria-labelledby attribute', () => {
+      fixture.componentInstance.ariaLabelledby = 'first-step-label';
+      fixture.detectChanges();
+
+      expect(stepHeader.getAttribute('aria-labelledby')).toBe('first-step-label');
+    });
+
+    it('should not be able to set both an aria-label and aria-labelledby', () => {
+      fixture.componentInstance.ariaLabel = 'First step';
+      fixture.componentInstance.ariaLabelledby = 'first-step-label';
+      fixture.detectChanges();
+
+      expect(stepHeader.getAttribute('aria-label')).toBe('First step');
+      expect(stepHeader.hasAttribute('aria-labelledby')).toBe(false);
+    });
+
+  });
 });
 
 /** Asserts that keyboard interaction works correctly. */
@@ -1158,3 +1199,16 @@ class LinearStepperWithValidOptionalStep {
   controls = [0, 0, 0].map(() => new FormControl());
   step2Optional = false;
 }
+
+
+@Component({
+  template: `
+    <mat-horizontal-stepper>
+      <mat-step [aria-label]="ariaLabel" [aria-labelledby]="ariaLabelledby" label="One"></mat-step>
+    </mat-horizontal-stepper>
+  `
+})
+class StepperWithAriaInputs {
+  ariaLabel: string;
+  ariaLabelledby: string;
+}