Hafeez, who scored an unbeaten 101 in Pakistan's 248-run win in the first Test in Abu Dhabi last week, joined fellow opener Ahmed Shehzad on the injury list.
Shehzad was hit by a Corey Anderson bouncer in the first Test and was ruled out of the remaining two matches.
Paceman Imran Khan was rested as third change in the side with openers Taufeeq Umar and Shan Masood, and paceman Ehsan Adil brought in.
The 21-year-old Adil played his only Test in South Africa last year.
New Zealand remained unchanged from the first Test.
Teams (from):
Pakistan: Misbah-ul Haq (capt), Taufeeq Umar, Shan Masood, Younis Khan, Asad Shafiq, Azhar Ali, Rahat Ali, Ehsan Adil, Sarfraz Ahmed, Zulfiqar Babar, Yasir Shah.
New Zealand: Brendon McCullum (capt), Tom Latham, Kane Williamson, Ross Taylor, Corey Anderson, BJ Watling, Jimmy Neesham, Mark Craig, Tim Southee, Trent Boult, Ish Sodhi.
Umpires: Paul Reiffel (AUS) and Ranmore Martinesz (SRI)
TV umpire: Rod Tucker (AUS)
Match referee: Andy Pycroft (ZIM)