My app runs on Ruby 2.0.0 built against OpenSSL 1.0.1c for AES-GCM support. Heroku appears to be using OpenSSL 0.9.8k (see https://twitter.com/sferik/status/3144953755558297
The solution to this problem is to create a custom buildpack.
You need to build a version of Ruby linked against the correct version of OpenSSL that will run on Heroku's system. For this, you need to use either a local 64-bit Linux system or a Heroku buildserver. Vulcan has problems building Ruby specifically, so the best way to do this in the absence of an appropriate local machine is to use Heroku push from an empty directory with a source-based buildpack. Then you can extract the binaries from the resulting slug and use them with a much faster binary buildpack.
I've posted my buildpack here. It is currently working and provides Ruby 2.0.0 with OpenSSL 1.0.1e.