diff --git a/src/cdk/a11y/aria-describer/aria-describer.ts b/src/cdk/a11y/aria-describer/aria-describer.ts
index ae31a20f575e..c84e81d3cbe8 100644
--- a/src/cdk/a11y/aria-describer/aria-describer.ts
+++ b/src/cdk/a11y/aria-describer/aria-describer.ts
@@ -85,7 +85,7 @@ export class AriaDescriber implements OnDestroy {
 
   /** Removes the host element's aria-describedby reference to the message element. */
   removeDescription(hostElement: Element, message: string|HTMLElement) {
-    if (!this._isElementNode(hostElement)) {
+    if (!message || !this._isElementNode(hostElement)) {
       return;
     }
 
diff --git a/src/material/tooltip/tooltip.ts b/src/material/tooltip/tooltip.ts
index c92e598bf966..b1b1d739065c 100644
--- a/src/material/tooltip/tooltip.ts
+++ b/src/material/tooltip/tooltip.ts
@@ -145,6 +145,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
   private _tooltipClass: string|string[]|Set<string>|{[key: string]: any};
   private _scrollStrategy: () => ScrollStrategy;
   private _viewInitialized = false;
+  private _pointerExitEventsInitialized = false;
 
   /** Allows the user to define the position of the tooltip relative to the parent element */
   @Input('matTooltipPosition')
@@ -175,7 +176,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
     if (this._disabled) {
       this.hide(0);
     } else {
-      this._setupPointerEvents();
+      this._setupPointerEnterEventsIfNeeded();
     }
   }
 
@@ -205,9 +206,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
   @Input('matTooltip')
   get message() { return this._message; }
   set message(value: string) {
-    if (this._message) {
-      this._ariaDescriber.removeDescription(this._elementRef.nativeElement, this._message);
-    }
+    this._ariaDescriber.removeDescription(this._elementRef.nativeElement, this._message);
 
     // If the message is not a string (e.g. number), convert it to a string and trim it.
     this._message = value != null ? `${value}`.trim() : '';
@@ -215,7 +214,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
     if (!this._message && this._isTooltipVisible()) {
       this.hide(0);
     } else {
-      this._setupPointerEvents();
+      this._setupPointerEnterEventsIfNeeded();
       this._updateTooltipMessage();
       this._ngZone.runOutsideAngular(() => {
         // The `AriaDescriber` has some functionality that avoids adding a description if it's the
@@ -241,7 +240,8 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
   }
 
   /** Manually-bound passive event listeners. */
-  private _passiveListeners = new Map<string, EventListenerOrEventListenerObject>();
+  private readonly _passiveListeners:
+      (readonly [string, EventListenerOrEventListenerObject])[] = [];
 
   /** Timer started at the last `touchstart` event. */
   private _touchstartTimeout: number;
@@ -283,7 +283,7 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
   ngAfterViewInit() {
     // This needs to happen after view init so the initial values for all inputs have been set.
     this._viewInitialized = true;
-    this._setupPointerEvents();
+    this._setupPointerEnterEventsIfNeeded();
 
     this._focusMonitor.monitor(this._elementRef)
       .pipe(takeUntil(this._destroyed))
@@ -312,10 +312,10 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
 
     // Clean up the event listeners set in the constructor
     nativeElement.removeEventListener('keydown', this._handleKeydown);
-    this._passiveListeners.forEach((listener, event) => {
+    this._passiveListeners.forEach(([event, listener]) => {
       nativeElement.removeEventListener(event, listener, passiveListenerOptions);
     });
-    this._passiveListeners.clear();
+    this._passiveListeners.length = 0;
 
     this._destroyed.next();
     this._destroyed.complete();
@@ -549,19 +549,46 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
   }
 
   /** Binds the pointer events to the tooltip trigger. */
-  private _setupPointerEvents() {
+  private _setupPointerEnterEventsIfNeeded() {
     // Optimization: Defer hooking up events if there's no message or the tooltip is disabled.
     if (this._disabled || !this.message || !this._viewInitialized ||
-        this._passiveListeners.size) {
+        this._passiveListeners.length) {
       return;
     }
 
     // The mouse events shouldn't be bound on mobile devices, because they can prevent the
     // first tap from firing its click event or can cause the tooltip to open for clicks.
-    if (!this._platform.IOS && !this._platform.ANDROID) {
+    if (this._platformSupportsMouseEvents()) {
       this._passiveListeners
-        .set('mouseenter', () => this.show())
-        .set('mouseleave', () => this.hide());
+          .push(['mouseenter', () => {
+            this._setupPointerExitEventsIfNeeded();
+            this.show();
+          }]);
+    } else if (this.touchGestures !== 'off') {
+      this._disableNativeGesturesIfNecessary();
+
+      this._passiveListeners
+          .push(['touchstart', () => {
+            // Note that it's important that we don't `preventDefault` here,
+            // because it can prevent click events from firing on the element.
+            this._setupPointerExitEventsIfNeeded();
+            clearTimeout(this._touchstartTimeout);
+            this._touchstartTimeout = setTimeout(() => this.show(), LONGPRESS_DELAY);
+          }]);
+    }
+
+    this._addListeners(this._passiveListeners);
+  }
+
+  private _setupPointerExitEventsIfNeeded() {
+    if (this._pointerExitEventsInitialized) {
+      return;
+    }
+    this._pointerExitEventsInitialized = true;
+
+    const exitListeners: (readonly [string, EventListenerOrEventListenerObject])[] = [];
+    if (this._platformSupportsMouseEvents()) {
+      exitListeners.push(['mouseleave', () => this.hide()]);
     } else if (this.touchGestures !== 'off') {
       this._disableNativeGesturesIfNecessary();
       const touchendListener = () => {
@@ -569,29 +596,35 @@ export class MatTooltip implements OnDestroy, AfterViewInit {
         this.hide(this._defaultOptions.touchendHideDelay);
       };
 
-      this._passiveListeners
-        .set('touchend', touchendListener)
-        .set('touchcancel', touchendListener)
-        .set('touchstart', () => {
-          // Note that it's important that we don't `preventDefault` here,
-          // because it can prevent click events from firing on the element.
-          clearTimeout(this._touchstartTimeout);
-          this._touchstartTimeout = setTimeout(() => this.show(), LONGPRESS_DELAY);
-        });
+      exitListeners.push(
+        ['touchend', touchendListener],
+        ['touchcancel', touchendListener],
+      );
     }
 
-    this._passiveListeners.forEach((listener, event) => {
+    this._addListeners(exitListeners);
+    this._passiveListeners.push(...exitListeners);
+  }
+
+  private _addListeners(
+      listeners: ReadonlyArray<readonly [string, EventListenerOrEventListenerObject]>) {
+    listeners.forEach(([event, listener]) => {
       this._elementRef.nativeElement.addEventListener(event, listener, passiveListenerOptions);
     });
   }
 
+  private _platformSupportsMouseEvents() {
+    return !this._platform.IOS && !this._platform.ANDROID;
+  }
+
   /** Disables the native browser gestures, based on how the tooltip has been configured. */
   private _disableNativeGesturesIfNecessary() {
-    const element = this._elementRef.nativeElement;
-    const style = element.style;
     const gestures = this.touchGestures;
 
     if (gestures !== 'off') {
+      const element = this._elementRef.nativeElement;
+      const style = element.style;
+
       // If gestures are set to `auto`, we don't disable text selection on inputs and
       // textareas, because it prevents the user from typing into them on iOS Safari.
       if (gestures === 'on' || (element.nodeName !== 'INPUT' && element.nodeName !== 'TEXTAREA')) {