Belgium and World Cup winners France are the first teams to share top spot in the FIFA rankings in the classification's 25-year history.
Roberto Martínez's side, defeated by Les Bleus in the semi-finals at Russia 2018 before claiming third place, overcame Scotland 4-0 in a friendly and won their Nations League debut 3-0 against Iceland earlier this month to join the world champions at the summit.
France, meanwhile, were held to a goalless draw by Germany in Munich before beating Netherlands 2-1 in Nations League Group A1.
Germany rise despite World Cup debacle
The only other change in the top 10 saw Denmark slip down one place to 10th, below Spain.
Despite their humiliating group-stage exit at the World Cup, Germany rose a further three positions and now sit 12th.
The biggest movers were Ukraine, who climbed six spots to 29th courtesy of Nations League triumphs over Czech Republic and Slovakia.