Former captain Ali's return meant there was no place in the 15-member squad for Shehzad, who failed to impress against Sri Lanka in the United Arab Emirates last month.
Pakistan won all five ODIs against Sri Lanka, but go into the five-match New Zealand series having lost eight of their last 11 ODI series.
"We kept the conditions in New Zealand in mind and the recent performances of some players in the domestic tournament," chief selector Inzamam-ul-Haq said after the squad announcement on Saturday.
Ali was rested for the Sri Lanka series, but is now fully fit after recovering from a knee problem, Haq added.
Fast bowler Junaid Khan has been ruled out of the New Zealand ODIs because of a fracture in his right foot, and Wasim failed a fitness test after reporting discomfort in his knee.
Fast bowler Aamer Yamin replaces Junaid in the squad.
Sarfraz Ahmed continues as captain, having led Pakistan to victory in the Champions Trophy in June.
Pakistan's first ODI against New Zealand is in Wellington on January 6. The two sides will also play three Twenty20s, for which Pakistan will make a separate squad announcement.
Pakistan - Sarfraz Ahmed (captain), Azhar Ali, Fakhar Zaman, Imam-ul-Haq, Babar Azam, Shoaib Malik, Mohammad Hafeez, Haris Sohail, Faheem Ashraf, Shadab Khan, Mohammad Nawaz, Mohammad Amir, Hasan Ali, Aamer Yamin, Rumman Raees.
First Published: December 23, 2017, 7:29 PM IST