The 2022 World Cup hosts' remarkable run at the continental championship, where they won all seven games and conceded only one goal, allowed them to move up 38 places from 93rd in the world.
Qatar beat regional heavyweights Saudi Arabia, Iraq and South Korea on their way to the final, where they stunned four-times champions Japan 3-1.
The Qataris are still only the fifth-highest ranked team from Asian Football Confederation, behind Iran (22), Japan (27), South Korea (38) and Australia (42).
Belgium continue to lead the world rankings ahead of last year's World Cup winners France and Brazil, with no changes to the top 20 due to the lack of fixtures involving teams from the European and South American confederations.