The changes were made from Bangladesh's last ODI series played against Zimbabwe back in May, which they lost 1-2.
Mashrafe's last ODI appearance was against West Indies last year after which he suffered a heel injury during this year's final of the BPL. This was the latest addition to his catalogue of leg injuries over the last 12 years, which has forced him to miss 103 ODIs during his career.
The only cricket behind him is the Dhaka Premier League where he 11 wickets from six matches at an average of 19.45 for Mohammedan Sporting Club.
Similar to Mashrafe, Naeem's last ODI was also against West Indies last year after which, like the pace bowler, he picked up an injury, on his quadriceps, during the BPL. He recovered sufficiently to tour England with the Bangladesh A side where he made a century, and has also played in the DPL.
The other two players included were Anamul, who skipped the Zimbabwe tour to attend college examinations, and Rubel who had to be withdrawn after the Test series there due to a bout of chicken pox.
Jahurul Islam is the only batsman who has been dropped from the team that lost the ODI series in Zimbabwe. He was out for a golden duck in the only game he played, and although he has been training with the Bangladesh Test squad off-late, Anamul was persisted with instead of him.
Robiul Islam has not also recovered adequately from a quadriceps injury that prevented him from playing in the ongoing Dhaka Test. Sajedul Islam has not been in form for quite a while now and is the other dropped player from the squad while Mohammad Ashraful is suspended pending a tribunal of alleged involvement in BPL corruption.
Bangladesh and New Zealand will play the first ODI on October 29 in Mirpur after the ongoing second Test.