Ferguson will take over the captain's role for the first time in his career as regular skipper Kane Williamson continues to recover from a knee injury, and his deputy Tom Latham has been rested for the series.
"Lockie is an experienced bowler at the international level, and this is an opportunity for him to really lead from the front with not just the bowling group but the team as a whole," coach Gary Stead said in a statement.
"He stepped into the role for the warm-up matches in England and led a group with a lot of moving parts well."
New Zealand also left out Devon Conway, Matt Henry, Daryl Mitchell, Glenn Phillips, Mitchell Santner and Tim Southee to keep them fresh for the 50-overs World Cup in India beginning on October 5.
Mark Chapman and Jimmy Neesham were not considered as they expect the arrival of their first children.
"Balancing workloads also provides opportunities and it's exciting to have different players in the group and learning in an environment like Bangladesh," said Stead.
"It can be a challenging place to tour and getting used to different conditions quickly will be important over the next few months."
Stead himself would stay back with batting coach Ronchi stepping in as the head coach for the Bangladesh tour.
All three one-dayers will be played in Mirpur between September 21-26.
New Zealand ODI squad: Lockie Ferguson (capt), Finn Allen, Tom Blundell, Trent Boult, Chad Bowes, Dane Cleaver, Dean Foxcroft, Kyle Jamieson, Cole McConchie, Adam Milne, Henry Nicholls, Rachin Ravindra, Ish Sodhi, Blair Tickner, Will Young.
