FIFA said Friday it is "proceeding with this investigation as a priority" from its security division's regional offices in Jordan and Malaysia.
"This will include interviewing some team players and coaching staff, the referees and other match officers," FIFA said in a statement. "It also involves assessing gambling activity on the match."
Lebanese referee Andre El Haddad sent off Indonesia's goalkeeper in the second minute and awarded Bahrain four penalties in the Feb. 29 match in Manama.
Bahrain's win raised suspicion because it trailed Qatar by three points and nine goals in group standings.
However, Qatar drew 2-2 in its final qualifier in Iran to advance to a further group-stage draw conducted Friday.
FIFA had written to Indonesian officials ahead of the match reminding them that World Cup rules require teams to field their strongest lineup.
Indonesia was expected to select an inexperienced team after suspending players from clubs in the breakaway Indonesian Super League.
It had lost all five previous group matches, conceding 16 goals while scoring just three.
The Asian Football Confederation has defended its member countries against any suspicions of match-fixing.
It issued a statement last week expressing confidence that the match was conducted properly, and that Bahrain was "tactically and technically" better.