The simplest way is to run webpack -p.
For an even smaller bundle, you probably want to run NODE_ENV=production webpack -p and tell React that you want a production build of the library by adding a custom plugin to your webpack config:
new webpack.DefinePlugin({
'process.env': {
'NODE_ENV': process.env.NODE_ENV !== 'production' ? JSON.stringify('development') : JSON.stringify('production'),
}
}),
Depending on whatever else you're doing in your webpack config, you may want to use process.env.NODE_ENV to enable/disable certain parts. I would highly recommend disabling sourcemaps in production. You can also create two separate webpack configs (one for dev and one for prod) and pass one in via webpack --config path/to/webpack.config.js.