For the three-match One-Day International series that starts in Napier on February 13, Taskin will be replaced by the experienced Safiul Islam.
Taskin has been ruled out of the tour with a torn ligament after he was recalled into both the ODI and Test squads following an impressive show in the ongoing Bangladesh Premier League (BPL) Twenty20 tournament.
He was the competition's leading wicket-taker with 22 scalps until he was hit by injury on Friday.
"We've chosen Ebadot for Test because he bowls hitting the seam. Shafiul will come into the ODI side as he is in fine form in BPL and he is also experienced," said chief selector Minhajul Abedin.
Newly called-up Ebadot was a finding of a talent hunt programme in 2017. The 25-year-old has claimed 59 wickets in 19 first-class matches.
Bangladesh will play three ODIs and three Test matches in New Zealand between February 13 and March 20.
This will be Bangladesh's first Test series abroad in 12 years, after their 2007 three-Test series in Sri Lanka when they lost all three matches.
Bangladesh also failed to win any matches during their last New Zealand tour in 2017-18.
ODI squad: Masrafe Mortaza (c), Shakib Al Hasan (vc), Tamim Iqbal Khan, Litton Das, Soumya Sarker, Mushfiqur Rahim, Mohammad Mithun, Mahmudullah, Sabbir Rahman, Mehidy Hasan, Mustafizur Rahman, Rubel Hossain, Mohammad Shaifuddin, Nayeem Hasan, Shafiul Islam
Test squad: Shakib Al Hasan (c), Mahmudullah (vc), Tamim Iqbal Khan, Shadman Islam, Mominul Haque, Mohammed Mithun, Mushfiqur Rahim, Litton Das, Mehidy Hasan, Taijul Islam, Mustafizur Rahman, Abu Jayed Rahi, Syed Khaled Ahmed, Nayeem Hasan, Ebadat Hossain
First Published: February 5, 2019, 5:27 PM IST