diff --git a/packages/babel-parser/src/plugins/estree.js b/packages/babel-parser/src/plugins/estree.js
index 71265770c2..e55071fbab 100644
--- a/packages/babel-parser/src/plugins/estree.js
+++ b/packages/babel-parser/src/plugins/estree.js
@@ -394,6 +394,8 @@ export default (superClass: Class<Parser>): Class<Parser> =>
         delete node.arguments;
         // $FlowIgnore - callee isn't optional in the type definition
         delete node.callee;
+      } else if (node.type === "CallExpression") {
+        (node: N.Node).optional = false;
       }
 
       return node;
@@ -434,4 +436,14 @@ export default (superClass: Class<Parser>): Class<Parser> =>
 
       return node;
     }
+
+    parseSubscript(...args) {
+      const node = super.parseSubscript(...args);
+
+      if (node.type === "MemberExpression") {
+        node.optional = false;
+      }
+
+      return node;
+    }
   };