diff --git a/packages/react-native-web/src/exports/Text/index.js b/packages/react-native-web/src/exports/Text/index.js
index de838bca..6dfdab96 100644
--- a/packages/react-native-web/src/exports/Text/index.js
+++ b/packages/react-native-web/src/exports/Text/index.js
@@ -62,7 +62,7 @@ class Text extends Component<*> {
 
     if (onPress) {
       otherProps.accessible = true;
-      otherProps.onClick = onPress;
+      otherProps.onClick = this._createPressHandler(onPress);
       otherProps.onKeyDown = this._createEnterHandler(onPress);
     }
 
@@ -89,6 +89,13 @@ class Text extends Component<*> {
       }
     };
   }
+
+  _createPressHandler(fn) {
+    return e => {
+      e.stopPropagation();
+      fn && fn(e);
+    };
+  }
 }
 
 const styles = StyleSheet.create({