Chris Coleman’s charges, who reached the last four in France in Wales’ first major tournament since 1958, were boosted by an increase of 291 ranking points, the highest of any nation in the football world.
Iceland, the smallest nation ever to have qualified for the European Championship and which has a population of just 330,000, saw their fairy-tale run end in the quarter-finals but saw their rankings jump 12 places to 22.
There were no changes in the top five rankings with Copa America finalists Argentina retaining top spot, followed by Belgium, Colombia, Germany and Chile.
Five-time world champions Brazil, who failed to progress past the group stages of Copa America for the first time since 1987, are on the brink of dropping out of the top 10, ranked at ninth, ahead of Italy.
European Championship finalists France jumped 10 places to move to seventh, one place behind winners Portugal.
Thailand, placed 121, are tops among South-east Asian nations, despite falling four places.
They are followed by the Philippines (135), and Vietnam (139). Malaysia (167) lie nine places below Singapore.
Asia’s top sides are Iran (39), South Korea (48), Japan (57), who fell by four places, and Australia (59).