I am looking for the same thing....if you have tried either of the suggestions above, and find that you are still stuck, consider this:
The MacBook Air has NO internal HD that might work in a standard external case. The MBA has solid state drives. The bus on the SSD card requires a PCIe-to-USB connection. I have not found one online, however, they are certainly available.
Restoring from the Backup would be the easiest thing to do...assuming that you are using a back up.
I will continue my search for the exact device and be sure that I place a link here when I find it.
OWC Envoy Pro Portable, Bus-Powered USB 3.0 Enclosure For Apple Flash SSDs
(June 2013-Current Mac Models)