Opener Imrul Kayes, middle-order batsman Naeem Islam and paceman Mahbubul Alam Robin were the newcomers in a 14-man squad for the three-match series starting here on Thursday.
The trio, belonging to the country's cricket academy, had consistently done well in domestic leagues and on overseas tours over the past one year, chief selector Rafiqul Alam told AFP.
"Kayes and Naeem are talented young batsmen while Robin has proved his worth as a medium-fast bowler. We have high hopes on them," he said.
The squad contains none of the 13 players who recently defected to the rebel Indian Cricket League (ICL), including seven current or former internationals.
The selectors also recalled wicket-keeper Mushfiqur Rahim, ignored for a recent one-day series in Australia, and fit-again seamer Syed Rasel.
Alam said the inexperienced squad was capable of causing an upset in the series.
"We hope we can win at least one match in the series," he said.
The Bangladesh Cricket Board has banned 13 players, including former captain Habibul Bashar, for 10 years for joining the ICL.
Daniel Vettori's New Zealanders will also play two Tests.
Bangladesh squad: Mohammad Ashraful (capt), Mashrafe Mortaza, Tamim Iqbal, Junaid Siddique, Imrul Kayes, Shakib Al Hasan, Mehrab Hossain, Naeem Islam, Mushfiqur Rahim, Mahmud Ullah Riyad, Abdur Razzak, Syed Rasel, Shahadat Hossain, Mahbubul Alam Robin.