diff --git a/src/cdk/stepper/stepper.ts b/src/cdk/stepper/stepper.ts
index 03cd15f597d..ae892d376ab 100644
--- a/src/cdk/stepper/stepper.ts
+++ b/src/cdk/stepper/stepper.ts
@@ -19,6 +19,7 @@ import {
   ContentChildren,
   Directive,
   EventEmitter,
+  ElementRef,
   forwardRef,
   Inject,
   Input,
@@ -31,6 +32,7 @@ import {
   ViewChild,
   ViewEncapsulation,
 } from '@angular/core';
+import {DOCUMENT} from '@angular/common';
 import {AbstractControl} from '@angular/forms';
 import {CdkStepLabel} from './step-label';
 import {Observable, Subject, of as obaservableOf} from 'rxjs';
@@ -164,6 +166,12 @@ export class CdkStepper implements AfterViewInit, OnDestroy {
   /** Used for managing keyboard focus. */
   private _keyManager: FocusKeyManager<FocusableOption>;
 
+  /**
+   * @breaking-change 8.0.0 Remove `| undefined` once the `_document`
+   * constructor param is required.
+   */
+  private _document: Document | undefined;
+
   /** The list of step components that the stepper is holding. */
   @ContentChildren(CdkStep) _steps: QueryList<CdkStep>;
 
@@ -218,8 +226,12 @@ export class CdkStepper implements AfterViewInit, OnDestroy {
 
   constructor(
     @Optional() private _dir: Directionality,
-    private _changeDetectorRef: ChangeDetectorRef) {
+    private _changeDetectorRef: ChangeDetectorRef,
+    // @breaking-change 8.0.0 `_elementRef` and `_document` parameters to become required.
+    private _elementRef?: ElementRef<HTMLElement>,
+    @Inject(DOCUMENT) _document?: any) {
     this._groupId = nextId++;
+    this._document = _document;
   }
 
   ngAfterViewInit() {
@@ -305,7 +317,14 @@ export class CdkStepper implements AfterViewInit, OnDestroy {
       selectedStep: stepsArray[newIndex],
       previouslySelectedStep: stepsArray[this._selectedIndex],
     });
-    this._keyManager.updateActiveItemIndex(newIndex);
+
+    // If focus is inside the stepper, move it to the next header, otherwise it may become
+    // lost when the active step content is hidden. We can't be more granular with the check
+    // (e.g. checking whether focus is inside the active step), because we don't have a
+    // reference to the elements that are rendering out the content.
+    this._containsFocus() ? this._keyManager.setActiveItem(newIndex) :
+                            this._keyManager.updateActiveItemIndex(newIndex);
+
     this._selectedIndex = newIndex;
     this._stateChanged();
   }
@@ -348,4 +367,15 @@ export class CdkStepper implements AfterViewInit, OnDestroy {
   private _layoutDirection(): Direction {
     return this._dir && this._dir.value === 'rtl' ? 'rtl' : 'ltr';
   }
+
+  /** Checks whether the stepper contains the focused element. */
+  private _containsFocus(): boolean {
+    if (!this._document || !this._elementRef) {
+      return false;
+    }
+
+    const stepperElement = this._elementRef.nativeElement;
+    const focusedElement = this._document.activeElement;
+    return stepperElement === focusedElement || stepperElement.contains(focusedElement);
+  }
 }
diff --git a/src/lib/stepper/stepper.spec.ts b/src/lib/stepper/stepper.spec.ts
index 3cb330ed073..7aa19ef3da5 100644
--- a/src/lib/stepper/stepper.spec.ts
+++ b/src/lib/stepper/stepper.spec.ts
@@ -259,6 +259,20 @@ describe('MatStepper', () => {
       expect(stepHeaderEl.focus).not.toHaveBeenCalled();
     });
 
+    it('should focus next step header if focus is inside the stepper', () => {
+      let stepperComponent = fixture.debugElement.query(By.directive(MatStepper)).componentInstance;
+      let stepHeaderEl = fixture.debugElement.queryAll(By.css('mat-step-header'))[1].nativeElement;
+      let nextButtonNativeEl = fixture.debugElement
+          .queryAll(By.directive(MatStepperNext))[0].nativeElement;
+      spyOn(stepHeaderEl, 'focus');
+      nextButtonNativeEl.focus();
+      nextButtonNativeEl.click();
+      fixture.detectChanges();
+
+      expect(stepperComponent.selectedIndex).toBe(1);
+      expect(stepHeaderEl.focus).toHaveBeenCalled();
+    });
+
     it('should only be able to return to a previous step if it is editable', () => {
       let stepperComponent = fixture.debugElement.query(By.directive(MatStepper)).componentInstance;
 
diff --git a/src/lib/stepper/stepper.ts b/src/lib/stepper/stepper.ts
index 250f2c816cc..df3358c2595 100644
--- a/src/lib/stepper/stepper.ts
+++ b/src/lib/stepper/stepper.ts
@@ -17,6 +17,7 @@ import {
   ContentChild,
   ContentChildren,
   Directive,
+  ElementRef,
   EventEmitter,
   forwardRef,
   Inject,
@@ -29,6 +30,7 @@ import {
   ViewEncapsulation,
 } from '@angular/core';
 import {FormControl, FormGroupDirective, NgForm} from '@angular/forms';
+import {DOCUMENT} from '@angular/common';
 import {ErrorStateMatcher} from '@angular/material/core';
 import {MatStepHeader} from './step-header';
 import {MatStepLabel} from './step-label';
@@ -147,8 +149,13 @@ export class MatHorizontalStepper extends MatStepper { }
   changeDetection: ChangeDetectionStrategy.OnPush,
 })
 export class MatVerticalStepper extends MatStepper {
-  constructor(@Optional() dir: Directionality, changeDetectorRef: ChangeDetectorRef) {
-    super(dir, changeDetectorRef);
+  constructor(
+    @Optional() dir: Directionality,
+    changeDetectorRef: ChangeDetectorRef,
+    // @breaking-change 8.0.0 `elementRef` and `_document` parameters to become required.
+    elementRef?: ElementRef<HTMLElement>,
+    @Inject(DOCUMENT) _document?: any) {
+    super(dir, changeDetectorRef, elementRef, _document);
     this._orientation = 'vertical';
   }
 }