Despite a 2-1 win over Thailand in their 2018 FIFA World Cup qualifier earlier this month, Ange Postecoglou's side suffered a fall off the back of their 2-0 loss to Japan in late August.
Australia will now play Syria, ranked a national team record 75th, in October's two-legged Asian World Cup qualifying playoff for the right to progress to an intercontinental playoff against the fourth-best team from the CONCACAF region.
Meanwhile, world champions Germany supplanted Brazil to return to the top of the pile.
Germany's 2-1 win away to the Czech Republic and their 6-0 drubbing of Norway in the World Cup qualifiers lifted them over the already-qualified Brazil, who dropped points in a draw away to Colombia.
European champions Portugal climbed three places to third, even though they are second in their World Cup qualifying group behind Switzerland.
Argentina are fourth in the rankings despite struggling in qualifying for Russia 2018 with draws in their past two games, away to Uruguay and at home to Venezuela.
Three other teams reached their best-ever place: Peru (12th), Northern Ireland (20th) and Luxemburg (101st) after they held France to a 0-0 draw away.
The rankings made disappointing reading for Asian nations with only three sides in the top 50: Iran (25th), Japan (40th) and Australia.
New Zealand, who will play off against the fifth-best team in South America for a World Cup berth, jumped 10 spots to 113th as Oceania's top nation.
The best of the other regions are Mexico (CONCACAF) at No.14 and Egypt (CAF) at No.30.
The next FIFA rankings will be announced on October 16 and will be used to determine the seedings in the draw for the four European playoff ties for next year's World Cup.
TOP 20 FIFA RANKINGS SEPTEMBER (last month's ranking in brackets)
1. Germany (2)
2. Brazil (1)
3. Portugal (6)
4. Argentina (3)
5. Belgium (9)
6. Poland (5)
7. Switzerland (4)
8. France (10)
9. Chile (7)
10. Colombia (8)
11. Spain (11)
12. Peru (15)
13. Wales (18)
14. Mexico (14)
15. England (13)
16. Uruguay (17)
17. Italy (12)
18. Croatia (16)
19. Slovakia (22)
20. Northern Ireland (23)
50. Australia (45)
113. New Zealand (123)