Adding to the valuable replies above:
You should check with the Indonesian Embassy/Consulate in Turkey for the document requirements to obtain the "Proof of Marriage Registration Abroad"-Letter. i.e. you will need passport photos (particular sizes..) etc., this list will be different from embassy to embassy so there is no alternative to checking with them directly (write an email).
The "Proof of Marriage Registration Abroad"-letter is called: "Surat Bukti Pencatatan Perkawinan di Luar Negeri". This is not the registration of your marriage in Indonesia yet! This is only one out of several documents that your spouse will have to provide to local administration after her return to Indonesia to register the marriage in Indonesia (i.e. you also need a sworn translation of the marriage certificate into Indonesian language etc.).
In Indonesia your marriage will be registered with KUA/Kantor Urusan Agama/Religious Affairs Office if you are both muslim. They are likely to ask proof of you being muslim and the marriage abroad being conducted in a muslim way. The document is called: "Pendaftaran Surat Bukti Perkawinan Warga Negar Indonesia Yang Dilangsungkan di Luar Negeri". This document is usally signed by both spouses, I am not sure whether they can produce this document without both spouses being present.
The marriage will be registered with Pencatatan Sipil/Civil Registration if it is a mixed-religion marriage.
Besides the other remarks already made (your wife needs complete set of new documents, national ID card, family card in order to sponsor your visa), one more strong recommendation:
Think already ahead and go through the full process to prepare documents for registration of your marriage to German authorities!
Only if it is registered in Germany, the German Embassy in Jakarta will be able to provide a confirmation letter late-on that your marriage is registered in Germany. You are likely to need this embassy-confirmation during KITAS or KITAP procedures. There are some reports on this forum, sometimes it is not asked for, but technically it is required. So you should think ahead concerning this even if you don't plan to ever live in Germany together with your wife (in which case you would of course also require the marriage to be registered, and hence the Apostille on the certificate of marriage.).
While Indonesia takes the special way to confirm the authenticity via the local embassy/consulate, Germany follows the more common way to request a legalization of the Turkish marriage certificate as proof that it is a real document (i.e. that stamp, signature etc. are true and match the registered specimens). Luckily for you, Turkey is (as well as Germany - but not Indonesia!) a participating country in the 1961 Hague Convention. Designated Competent authorities, which means you only need a "simple legalization" called apostille or apostillation.
Legalization: document goes to Justice Ministry for verification, then to Foreign Ministry, then to your local Embassy abroad. This is what all Indonesian documents need to go through to be accepted abroad.
Apostillation: document only goes to Justice Ministry for verification and will be recognized by authorities of participating states (i.e. your local administration back in Germany).
So you need to check the apostillation process in Turkey and get the apostille sticker before leaving the country (or using legal service for this if available and you like to entrust them the original document and you are in a rush). Of course you could also come back to Turkey and do this later... but it does not make much sense as you will be already there. With the apostille on your marriage certificate and a fully legalized translation of all the documents of your wife (because Indonesia does not take part in apostille, see above), you can register your marriage in Germany.
One final word of advise concerning this: register the marriage in Germany via German Embassy in Jakarta once you finished the visa procedures and are living in Indonesia. They accept a German translation of your wife's legalized documents by a translator registered with the German Embassy, it's quite cheap and easy to do. The embassy does the document checking quite straight-forward and confirms to German authorities + sends a copy to them. Then everything is processed at the Standesamt of your last residential address in Germany. You keep the originals with you all the time.
If you register directly with the German authorities you will need to go through a translator that is sworn-in by higher courts in Germany, driving up costs, processing times + they will scrutinize everything much more than the German Embassy + you need to give the original documents away or even send them around the globe.
Good luck, it's quite an adventure and you will be rewarded with even more memories.