Yes, it's from Islamic Arabic. There's a bunch of Bahasa phrases that came by that route - including the more complete Asalamualaikum, the reply Walaikumsalam, and Inshallah (god willing). (not sure on the spellings here)
I guess being something like 80% Muslim-majority, it's not really surprising some Islamic phrases get adopted into the general language. English has done the same with a bunch of Christianity-derived phrases - things like "Bless you" as the response to a sneeze.
Just like the "bless you" case, the use in Bahasa seems to have diverged a bit from the the strict Islamic interpretation, and can be used by non-Muslims.
Especially for "inshallah", it's diverged quite a bit, and has become almost a way to politely dismiss an obligation:
"Will you come back (next week, etc)?" "Inshallah"
Literally meaning- "if god wills" But more colloquially; it's more of a "I might, but won't make a commitment to it" - or even "probably not"