Nicknamed "The Fizz", the 21-year-old left-arm pacer missed the recent home series against England recovering from shoulder surgery that he underwent in Britain on August 10.
Rahman aggravated an old shoulder injury in July during his short stint with English county side Sussex in the Twenty20 Blast competition when he could only play in two matches before being sidelined.
"He has already started bowling in the nets and we hope he will be fully fit before our New Zealand series starts," said selector Habibul Bashar.
Prior to the visit, Bangladesh will hold a camp in Sydney where they will play two Twenty20 warm-up matches against local teams Sydney Sixers and Sydney Thunders.
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Selectors included Rahman in Bangladesh's 20-member squad for the Australia and New Zealand trip that was announced late on Friday.
Unheralded Tanveer Haider is the only surprise inclusion in the squad, which also retained paceman Subashis Roy, who was in the squad for the recent second Test against England but did not play.
"We were looking for a good leg spinner for quite some time. We hope Tanveer would deliver it," said Bashar about the 24-year-old who has six first-class centuries.
Selectors also included uncapped pacer Ebadat Hossain and teenage batsman Nazmul Hossain as a developing prospect though they are not officially part of the squad.
The squad did not include batsman Nasir Hossain and pacemen Al-Amin Hossain and Rubel Hossain in the team.
Bangladesh squad for New Zealand tour: Tamim Iqbal, Imrul Kayes, Mominul Haque, Mahmudullah Riyad, Shakib Al Hasan, Mushfiqur Rahim, Sabbir Rahman, Soumya Sarkar, Mosaddek Hossain, Nurul Hassan, Mehedi Hasan, Shuvagata Hom, Taijul Islam, Mashrafe Mortaza, Mustafizur Rahman, Taskin Ahmed, Shafiul Islam, Subashis Roy, Mohammad Shahid and Tanveer Haider.