diff --git a/src/cdk/stepper/stepper.ts b/src/cdk/stepper/stepper.ts
index cac528d64a4f..da2b61dd018c 100644
--- a/src/cdk/stepper/stepper.ts
+++ b/src/cdk/stepper/stepper.ts
@@ -293,12 +293,11 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
 
     if (this.steps && this._steps) {
       // Ensure that the index can't be out of bounds.
-      if ((newIndex < 0 || newIndex > this.steps.length - 1) &&
-        (typeof ngDevMode === 'undefined' || ngDevMode)) {
+      if (!this._isValidIndex(index) && (typeof ngDevMode === 'undefined' || ngDevMode)) {
         throw Error('cdkStepper: Cannot assign out-of-bounds value to `selectedIndex`.');
       }
 
-      if (this._selectedIndex != newIndex && !this._anyControlsInvalidOrPending(newIndex) &&
+      if (this._selectedIndex !== newIndex && !this._anyControlsInvalidOrPending(newIndex) &&
           (newIndex >= this._selectedIndex || this.steps.toArray()[newIndex].editable)) {
         this._updateSelectedItemIndex(index);
       }
@@ -365,6 +364,13 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
         this._selectedIndex = Math.max(this._selectedIndex - 1, 0);
       }
     });
+
+    // The logic which asserts that the selected index is within bounds doesn't run before the
+    // steps are initialized, because we don't how many steps there are yet so we may have an
+    // invalid index on init. If that's the case, auto-correct to the default so we don't throw.
+    if (!this._isValidIndex(this._selectedIndex)) {
+      this._selectedIndex = 0;
+    }
   }
 
   ngOnDestroy() {
@@ -525,6 +531,11 @@ export class CdkStepper implements AfterContentInit, AfterViewInit, OnDestroy {
     return stepperElement === focusedElement || stepperElement.contains(focusedElement);
   }
 
+  /** Checks whether the passed-in index is a valid step index. */
+  private _isValidIndex(index: number): boolean {
+    return index > -1 && (!this.steps || index < this.steps.length);
+  }
+
   static ngAcceptInputType_editable: BooleanInput;
   static ngAcceptInputType_optional: BooleanInput;
   static ngAcceptInputType_completed: BooleanInput;
diff --git a/src/material/stepper/stepper.spec.ts b/src/material/stepper/stepper.spec.ts
index 04377c66c563..8c05870055c9 100644
--- a/src/material/stepper/stepper.spec.ts
+++ b/src/material/stepper/stepper.spec.ts
@@ -29,6 +29,7 @@ import {
   Provider,
   ViewChildren,
   QueryList,
+  ViewChild,
 } from '@angular/core';
 import {ComponentFixture, fakeAsync, flush, inject, TestBed} from '@angular/core/testing';
 import {
@@ -1270,6 +1271,24 @@ describe('MatStepper', () => {
     expect(steppers[0].steps.length).toBe(3);
     expect(steppers[1].steps.length).toBe(2);
   });
+
+  it('should not throw when trying to change steps after initializing to an out-of-bounds index',
+    () => {
+      const fixture = createComponent(StepperWithStaticOutOfBoundsIndex);
+      fixture.detectChanges();
+      const stepper = fixture.componentInstance.stepper;
+
+      expect(stepper.selectedIndex).toBe(0);
+      expect(stepper.selected).toBeTruthy();
+
+      expect(() => {
+        stepper.selectedIndex = 1;
+        fixture.detectChanges();
+      }).not.toThrow();
+
+      expect(stepper.selectedIndex).toBe(1);
+      expect(stepper.selected).toBeTruthy();
+    });
 });
 
 /** Asserts that keyboard interaction works correctly. */
@@ -1780,3 +1799,17 @@ class StepperWithNgIf {
 class NestedSteppers {
   @ViewChildren(MatStepper) steppers: QueryList<MatStepper>;
 }
+
+
+@Component({
+  template: `
+    <mat-vertical-stepper selectedIndex="1337">
+      <mat-step label="Step 1">Content 1</mat-step>
+      <mat-step label="Step 2">Content 2</mat-step>
+      <mat-step label="Step 3">Content 3</mat-step>
+    </mat-vertical-stepper>
+  `
+})
+class StepperWithStaticOutOfBoundsIndex {
+  @ViewChild(MatStepper) stepper: MatStepper;
+}