Allrounder Chigumbura said yesterday "it's the best time to leave it to the next guy to lead us."
Zimbabwe won the last two games to salvage a draw in Bangladesh.
The 29-year-old Chigumbura said he still wanted to contribute to the team as a senior player.
His leadership was heavily criticised when Zimbabwe lost 3-2 to minnow Afghanistan in their one-day international series late last year.
Chigumbura's resignation coincided with former captain Brendan Taylor saying he would consider returning to play for Zimbabwe after his contract with English county team Nottinghamshire expires.