Afridi has been out of action since suffering a knee injury during the Twenty20 World Cup final in Melbourne on November 13. Naseem and Haris (thigh) played the first test against England but missed the last two matches.
"Haris Rauf has not been included in the squad as he is recovering from an injury he sustained while fielding in the Rawalpindi test," the Pakistan Cricket Board said in a statement on Wednesday.
"However, fast bowler Naseem Shah, who missed the Multan and Karachi tests due to a shoulder niggle, has been being declared fit and as such, retained in the squad."
Pakistan have also recalled fast bowler Hasan Ali and picked uncapped middle-order batter Kamran Ghulam to replace Azhar Ali, who retired after the team's 3-0 series whitewash by England.
The upcoming series marks the beginning of Tim Southee's reign as New Zealand test captain after he took over from Kane Williamson, who ended his six-year tenure earlier this month.
Karachi hosts the first test from Monday, while the second match is scheduled for Multan.
The teams will then return to Karachi to play three one-day internationals.
Pakistan: Babar Azam (captain), Abdullah Shafique, Abrar Ahmed, Agha Salman, Hasan Ali, Imam-ul-Haq, Kamran Ghulam, Mohammad Nawaz, Mohammad Rizwan, Mohammad Wasim, Naseem Shah, Nauman Ali, Sarfaraz Ahmed, Saud Shakeel, Shan Masood, Zahid Mehmood
