Pakistan have 1,427 ranking points and are now behind Sri Lanka, who occupy seventh place with 1,222 points.
Pakistan suffered an innings-and-103-run defeat against England on Friday. After conceding a 238-run first-innings lead, the visitors were bowled out for just 135 in their second innings.
Bangladesh's rise came after their historic away series against Australia ended in a 1-1 draw. They secured their first-ever Test victory on Australian soil by defeating the hosts by nine wickets in the opening Test at Marrara Stadium.
The result pushed both Pakistan and Sri Lanka down the rankings.
Australia remain at the top of the Test rankings, followed by South Africa and New Zealand. India and England occupy fourth and fifth positions respectively.
Pakistan's defeat also pushed them back to the bottom of the ICC World Test Championship (WTC) 2025-27 standings.
Pakistan have won only two of their seven WTC matches and lost five, leaving them with a points percentage of 19.05.
Australia lead the WTC standings after winning eight of their 10 matches and losing two. They have 96 points and a points percentage of 80%.
Defending champions South Africa are second with three wins from four matches, earning 36 points at a points percentage of 75%.
