To enable access over HTTPS Dokku provides a Let’s Encrypt plugin.

First, I installed the plugin by running sudo dokku plugin:install https://github.com/dokku/dokku-letsencrypt.git

Then it was a matter of setting an email for the app (last command) and running

$ dokku letsencrypt:enable test-app

And that was it! The test app is available via HTTPS at https://test-app.<domain.co>

Letsencrypt commands

Additional commands:
    letsencrypt:active                      Verify if letsencrypt is active for an app
    letsencrypt:auto-renew []               Auto-renew app if renewal is necessary
    letsencrypt:cleanup                     Remove stale certificate directories for app
    letsencrypt:cron-job [--add --remove]        Add or remove a cron job that periodically calls auto-renew.
    letsencrypt:disable                     Disable letsencrypt for an app
    letsencrypt:enable                      Enable or renew letsencrypt for an app
    letsencrypt:help                             Display letsencrypt help
    letsencrypt:list                             List letsencrypt-secured apps with certificate expiry times
    letsencrypt:revoke                      Revoke letsencrypt certificate for app
    letsencrypt:set   ()   Set or clear a letsencrypt property for an app