The preferred way of getting extensions for Heroku would be to use composer.json. mbstring is one of the extensions that Heroku provides pre-compiled and shared according to https://devcenter.heroku.com/articles/php-support#extensions
To use it, all you have to do is create a composer.json file (if you don't already have one) in the root of your project with the following contents:
{
"require": {
"ext-mbstring": "*"
}
}
There is no need to compile your own mbstring extension or grab a compiled version from somewhere else.
As a side note, there's also no longer a need to compile the MongoDB extension yourself, either. It's also on the list of Heroku-provided extensions and you could have a composer.json file do both, like this:
{
"require": {
"ext-mbstring": "*",
"ext-mongo": "*"
}
}