I agree with the previous answers, the key two elements you should work on to get an internship in Asia area:
- Target a country where language is not an issue
- Manage to find a referral for your application
Also, you should keep in mind that in case you manage to join a firm, you may find challenging to network internally with colleagues and senior consultants due to the language barrier. This could create a problem for your career growth until you become fluent in the local language.
Given the previous points, some options you may consider are:
- Target Singapore, where English is one of the official languages (expect strong competition there though)
- Target Australia joining a company with offices in Asia, then move to Asia after 1-2 years with internal relocation (assuming you want to stay in Asia in the long run)
- Target Germany joining a company with offices in Asia, then move to Asia after 1-2 years with internal relocation (assuming you want to stay in Asia in the long run). If that turns out unfeasible due to the distance, you may consider an MBA in Asia in a business school with a strong brand name (eg Insead)
For all the three options, as mentioned, having a referral could help a lot.
Hope this helps,