The Socceroos are now fourth among Asian Football Confederation nations, with Japan (No.53) and Korea (No.50) both overtaking them and Iran up three spots to 39.
A largely experimental Australian side went down 2-1 to England at The Stadium of Light last week.
The Socceroos will have the chance to accrue rankings points with wins over Greece in their two-match series starting in Sydney on Saturday and concluding in Melbourne on Tuesday.
Meanwhile, Argentina will kick off the Copa America as the world's top-ranked team, and No.2 Belgium goes to the European Championship as the best on their continent.
Colombia, who open the Copa America against hosts United States, moved up one place to No.3. Germany are No. 4 while defending Copa America champions Chile dropped two places to No.5 - before they play Argentina in their tournament opener.
Mexico are the top-ranked CONCACAF team at No.16. The United States dropped two to No.31.
EURO 2016 host France climbed four to No.17 after beating Cameroon in a warm-up this week.
Algeria are the top African nation at No.32.
FIFA men's world rankings
1. (1) Argentina 1,503 points
2. (2) Belgium 1,384
3. (4) Colombia 1,328
4. (5) Germany 1,310
5. (3) Chile 1,293
6. (6) Spain 1,267
7. (7) Brazil 1,257
8. (8) Portugal 1,181
9. (9) Uruguay 1,158
10. (11) Austria 1,077
59. (50) Australia 563