diff --git a/src/demo-app/table/table-demo.html b/src/demo-app/table/table-demo.html
index 0433ee7f1ad7..ba16cef3301e 100644
--- a/src/demo-app/table/table-demo.html
+++ b/src/demo-app/table/table-demo.html
@@ -65,7 +65,7 @@ <h3>CdkTable Example</h3>
     <!-- Column Definition: ID -->
     <ng-container cdkColumnDef="userId">
       <cdk-header-cell *cdkHeaderCellDef
-                       mat-sort-header arrowPosition="before">
+                       mat-sort-header arrowPosition="before" disabled>
         ID
       </cdk-header-cell>
       <cdk-cell *cdkCellDef="let row"> {{row.id}} </cdk-cell>
@@ -228,7 +228,7 @@ <h3>MatTable With MatTableDataSource Example</h3>
 
     <!-- Column Definition: ID -->
     <ng-container cdkColumnDef="userId">
-      <mat-header-cell *matHeaderCellDef mat-sort-header> ID </mat-header-cell>
+      <mat-header-cell *matHeaderCellDef mat-sort-header disabled> ID </mat-header-cell>
       <mat-cell *matCellDef="let row"> {{row.id}} </mat-cell>
     </ng-container>
 
diff --git a/src/lib/sort/sort-header.html b/src/lib/sort/sort-header.html
index 4061041b1930..a2f6633d3ff9 100644
--- a/src/lib/sort/sort-header.html
+++ b/src/lib/sort/sort-header.html
@@ -1,6 +1,9 @@
 <div class="mat-sort-header-container"
+     [class.mat-sort-header-disabled]="disabled"
      [class.mat-sort-header-position-before]="arrowPosition == 'before'">
+
   <button class="mat-sort-header-button" type="button"
+          [disabled]="disabled"
           [attr.aria-label]="_intl.sortButtonLabel(id)">
     <ng-content></ng-content>
   </button>
diff --git a/src/lib/sort/sort-header.scss b/src/lib/sort/sort-header.scss
index 088a5429f68e..6c7560e00b67 100644
--- a/src/lib/sort/sort-header.scss
+++ b/src/lib/sort/sort-header.scss
@@ -26,6 +26,11 @@ $mat-sort-header-arrow-transition: 225ms cubic-bezier(0.4, 0, 0.2, 1);
   color: currentColor;
 }
 
+.mat-sort-header-disabled,
+.mat-sort-header-button[disabled] {
+  cursor: default;
+}
+
 .mat-sort-header-arrow {
   height: $mat-sort-header-arrow-container-size;
   width: $mat-sort-header-arrow-container-size;
diff --git a/src/lib/sort/sort-header.ts b/src/lib/sort/sort-header.ts
index 67e395b3906e..a0b5aed3ab59 100644
--- a/src/lib/sort/sort-header.ts
+++ b/src/lib/sort/sort-header.ts
@@ -15,25 +15,28 @@ import {
   ViewEncapsulation
 } from '@angular/core';
 import {coerceBooleanProperty} from '@angular/cdk/coercion';
-import {
-  trigger,
-  state,
-  style,
-  animate,
-  transition,
-  keyframes,
-} from '@angular/animations';
+import {animate, keyframes, state, style, transition, trigger} from '@angular/animations';
 import {CdkColumnDef} from '@angular/cdk/table';
 import {Subscription} from 'rxjs/Subscription';
 import {merge} from 'rxjs/observable/merge';
 import {MatSort, MatSortable} from './sort';
 import {MatSortHeaderIntl} from './sort-header-intl';
 import {getSortHeaderNotContainedWithinSortError} from './sort-errors';
-import {AnimationCurves, AnimationDurations} from '@angular/material/core';
+import {
+  AnimationCurves,
+  AnimationDurations,
+  CanDisable,
+  mixinDisabled
+} from '@angular/material/core';
 
 const SORT_ANIMATION_TRANSITION =
     AnimationDurations.ENTERING + ' ' + AnimationCurves.STANDARD_CURVE;
 
+// Boilerplate for applying mixins to MatSortHeader.
+/** @docs-private */
+export class MatSortHeaderBase { }
+export const _MatSortHeaderMixinBase = mixinDisabled(MatSortHeaderBase);
+
 /**
  * Applies sorting behavior (click to change sort) and styles to an element, including an
  * arrow to display the current sort direction.
@@ -49,8 +52,9 @@ const SORT_ANIMATION_TRANSITION =
   exportAs: 'matSortHeader',
   templateUrl: 'sort-header.html',
   styleUrls: ['sort-header.css'],
+  inputs: ['disabled'],
   host: {
-    '(click)': '_sort.sort(this)',
+    '(click)': '_handleClick()',
     '[class.mat-sort-header-sorted]': '_isSorted()',
   },
   encapsulation: ViewEncapsulation.None,
@@ -93,7 +97,7 @@ const SORT_ANIMATION_TRANSITION =
     ])
   ]
 })
-export class MatSortHeader implements MatSortable {
+export class MatSortHeader extends _MatSortHeaderMixinBase implements MatSortable, CanDisable {
   private _rerenderSubscription: Subscription;
 
   /**
@@ -118,6 +122,8 @@ export class MatSortHeader implements MatSortable {
               changeDetectorRef: ChangeDetectorRef,
               @Optional() public _sort: MatSort,
               @Optional() public _cdkColumnDef: CdkColumnDef) {
+    super();
+
     if (!_sort) {
       throw getSortHeaderNotContainedWithinSortError();
     }
@@ -140,6 +146,13 @@ export class MatSortHeader implements MatSortable {
     this._rerenderSubscription.unsubscribe();
   }
 
+  /** Triggers the sort on this sort header if it is not disabled. */
+  _handleClick() {
+    if (!this.disabled) {
+      this._sort.sort(this);
+    }
+  }
+
   /** Whether this MatSortHeader is currently sorted in either ascending or descending order. */
   _isSorted() {
     return this._sort.active == this.id &&
diff --git a/src/lib/sort/sort.spec.ts b/src/lib/sort/sort.spec.ts
index 59d3f8df9c8a..ceb014e82425 100644
--- a/src/lib/sort/sort.spec.ts
+++ b/src/lib/sort/sort.spec.ts
@@ -52,7 +52,7 @@ describe('MatSort', () => {
 
   it('should have the sort headers register and deregister themselves', () => {
     const sortables = component.matSort.sortables;
-    expect(sortables.size).toBe(4);
+    expect(sortables.size).toBe(5);
     expect(sortables.get('defaultSortHeaderA')).toBe(component.matSortHeaderDefaultA);
     expect(sortables.get('defaultSortHeaderB')).toBe(component.matSortHeaderDefaultB);
 
@@ -60,11 +60,26 @@ describe('MatSort', () => {
     expect(sortables.size).toBe(0);
   });
 
+  it('should be able to disable a sort header', () => {
+    // With it disabled, it should not set to active
+    fixture.componentInstance.sort('sortF');
+    fixture.detectChanges();
+    expect(component.matSort.active).toBe(undefined);
+
+    // Set disabled to false
+    fixture.componentInstance.disableSortF = false;
+    fixture.detectChanges();
+
+    // Sort should work
+    fixture.componentInstance.sort('sortF');
+    fixture.detectChanges();
+    expect(component.matSort.active).toBe('sortF');
+  });
+
   it('should use the column definition if used within a cdk table', () => {
     let cdkTableMatSortAppFixture = TestBed.createComponent(CdkTableMatSortApp);
     let cdkTableMatSortAppComponent = cdkTableMatSortAppFixture.componentInstance;
 
-    cdkTableMatSortAppFixture.detectChanges();
     cdkTableMatSortAppFixture.detectChanges();
 
     const sortables = cdkTableMatSortAppComponent.matSort.sortables;
@@ -78,7 +93,6 @@ describe('MatSort', () => {
     let matTableMatSortAppFixture = TestBed.createComponent(MatTableMatSortApp);
     let matTableMatSortAppComponent = matTableMatSortAppFixture.componentInstance;
 
-    matTableMatSortAppFixture.detectChanges();
     matTableMatSortAppFixture.detectChanges();
 
     const sortables = matTableMatSortAppComponent.matSort.sortables;
@@ -223,6 +237,7 @@ function testSingleColumnSortDirectionSequence(fixture: ComponentFixture<SimpleM
       </div>
       <div id="overrideStart" mat-sort-header="overrideStart" start="desc"> D </div>
       <div id="overrideDisableClear" mat-sort-header="overrideDisableClear" disableClear> E </div>
+      <div id="sortF" mat-sort-header="sortF" [disabled]="disableSortF"> F </div>
     </div>
   `
 })
@@ -232,6 +247,7 @@ class SimpleMatSortApp {
   active: string;
   start: SortDirection = 'asc';
   direction: SortDirection = '';
+  disableSortF = true;
   disableClear: boolean;
 
   @ViewChild(MatSort) matSort: MatSort;
@@ -246,7 +262,6 @@ class SimpleMatSortApp {
   }
 }
 
-
 class FakeDataSource extends DataSource<any> {
   connect(collectionViewer: CollectionViewer): Observable<any[]> {
     return map.call(collectionViewer.viewChange, () => []);