@index.html
<link rel="shortcut icon" type="image/x-icon" href="./favicon.ico">

@package.json
"devDependencies": {
    ...
    "favicons-webpack-plugin": "0.0.7",
    ...
}

@webpack.config.js
const FaviconsWebpackPlugin = require('favicons-webpack-plugin');
...
plugins: [HTMLWebpackPluginConfig, new FaviconsWebpackPlugin(__dirname + '/app/favicon.png')],
...
module: {
    loaders: [
      ...
      {
        test: /\.ico$|\.jpe?g$|\.gif$|\.png$|\.svg$/,
        loader: 'file-loader?name=[name].[ext]'
      },
      ...