In the two games played by the side since March's rankings were announced, Russia beat Azerbaijan 2-0 at home and Lichtenstein 1-0 away in World Cup qualifiers. They were overtaken by England, who won two home matches, beating Slovakia 4-0 in a friendly and Ukraine 2-1 in a qualifier. England also overtook Croatia to jump to seventh place.
Russia's next match is against Finland, ranked 51st, on June 10 in Helsinki in a World Cup qualifier.
The top three positions in the rankings remain unchanged, with Spain followed by Germany and the Netherlands, respectively. Brazil swapped positions with Italy to move up to fifth from fourth.
The biggest climbers were Bosnia-Herzegovina, who moved up 20 places to 38th after home and away victories over Belgium in World Cup qualifiers.
Last place, 202nd, is shared by six countries - San Marino, Anguilla, Montserrat, American Samoa, the Cook Islands, and Papua New Guinea.
Top 10 (last month's position in brackets.)
1. Spain (1)
2. Germany (2)
3. Netherlands (3)
4. Brazil (5)
5. Italy (4)
6. Argentina (6)
7. England (9)
8. Croatia (7)
9. Russia (8)
10. France (12)