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 UAE last month.
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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 Inzamamul 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.
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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-bowling all-rounder 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 T20Is, for which Pakistan will make a separate squad announcement.
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