Heroku is PasS environment which supports PHP unofficially. It is missing some of extensions initially. One instance is mbstring.　However I noticed that mbstring is able to build on heroku run bash and can be loaded from project local php.ini configuration.
I put the mbstring.so on github. If you need it, just copy into your project and put php.ini which include:

extension=/app/www/mbstring.so

Example

This application is running on heroku with mbstring.

Enjoy php on heroku!