Sharjeel, 27, is better known for his power hitting in 20 ODIs and 15 T20 internationals and this is his first selection in a Test series.
Besides left-handed Sharjeel, Pakistani selectors have also included wicketkeeper-batsman Mohammad Rizwan in the Test squad.
"The Test team has been selected keeping in mind the conditions in New Zealand and the recent performances of players in the recent Test series against England and West Indies. The team is a fine blend of experience and youth, and the selectors have stick to the same combination of players selected against England and West Indies series earlier and believe that team will do well in the tour," chief selector Inzamam-ul-Haq said in a statement.
This effectively means that the selectors will decide later on the touring squad for the Test series in Australia in December.
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Reliable sources said that the selectors decided to ignore Hafeez after he failed a bowling test at the PCB's biomechanic lab in Lahore.
"Basically the selectors wanted to see if Hafeez could clear the preliminary bowling assessment test in Lahore after which the PCB would have sent him for the ICC bowling assessment test in England," one source said.
Hafeez has not been able to bowl since mid-2015 after the ICC declared his bowling action illegal.
The first Test match between Pakistan and New Zealand will be played from November 17-21 at Hagley Oval, Christchurch followed by second Test from November 25 to 29 at Seddon Park, Hamilton.
Veteran spinner Zulfiqar Babar is the only player to have be en dropped from the squad that is presently playing against the West Indies in Sharjah.