How can I use async/await in a es6 javascript class?

So I'm trying to make a function of a class I made async, but webpack gives me an error when compiling the class.

My code would be something like this:

class MyClass {

   constructor(apiService) {
       this._apiService = apiService;
   }

   async updateInformation() {
       await this._apiService.updateInformation();
       // .. do more stuff I have to do 
   }
}

The error that webpack gives me is:

Module build failed: SyntaxError: Unexpected token

(The Unexpected token points to the 'u' after async)