For Vue CLI 3 it is pretty simple.
Edit your vue.config.js (if there is none, create it in project root directory) and add following lines:
module.exports = {
baseUrl: "./"
};
Or whatever sub-directory you want.
You may also decide according to NODE_ENV. See the docs.
module.exports = {
baseUrl: process.env.NODE_ENV === 'production'
? '/production-sub-path/'
: "https://stackoverflow.com/"
}
UPDATE
As mentioned in comments below, for Vue CLI 3.3+ use publicPath property instead of baseUrl.