Bangladesh moved up three places after their two-match series against Australia ended 1-1.
In the latest rankings released following the conclusion of the Mackay Test on Sunday, Najmul Hossain Shanto's side have 78 rating points from 24 matches, with 1,878 total points.
Australia remain firmly at the top with 126 rating points, followed by South Africa on 119. New Zealand, India and England occupy third, fourth and fifth places respectively.
Bangladesh's rise was largely powered by their historic victory in the first Test in Darwin.
The Tigers defeated Australia by nine wickets, securing their first-ever Test win on Australian soil and only their second victory against Australia in the format.
They were unable to maintain that momentum in Mackay, however, suffering a heavy innings-and-51-run defeat inside two days after a major batting collapse. Despite the loss, the series draw was enough to lift Bangladesh three places in the rankings.
Holding on to sixth place, though, will be a challenge. Bangladesh's 78 rating points put them only marginally ahead of the next three teams.
Sri Lanka have 76, Pakistan 75 and West Indies 74, occupying seventh, eighth and ninth places respectively. With such a narrow gap, Bangladesh could quickly drop back down the rankings with a poor result.
Before this latest rise, Bangladesh's highest-ever position in the Test rankings was seventh. They first reached that spot in May this year after whitewashing Pakistan 2-0 in a two-Test home series.
However, Bangladesh failed to hold on to seventh after subsequently losing an away Test against Zimbabwe.
The latest rise to sixth represents another significant milestone for Bangladesh as they continue to establish themselves among the stronger Test teams in world cricket.
