Pakistan named uncapped 24-year-old batsman Imran Butt in its 15-member squad for the first test. Butt scored 934 runs in the 2019-20 first class tournament at an average of 62 with four centuries and three half centuries.
In the absence of Azam, Pakistan trails 2-0 in the three-match Twenty20 series against New Zealand with the last game due to be played at Napier on Tuesday.
"It will be nearly two weeks to Babar's injury when the first test starts, (but) it will be hard on him and the team to play him without any net sessions," Pakistan head coach Misbah-ul-Haq said.
"I remain confident and optimistic that other players will rise to the occasion in Mount Maunganui and … put the disappointment of the T20I series behind them."
Pakistan squad:
Mohammad Rizwan (captain), Abid Ali, Azhar Ali, Faheem Ashraf, Fawad Alam, Haris Sohail, Imran Butt, Mohammad Abbas, Naseem Shah, Sarfaraz Ahmed, Shadab Khan, Shaheen Afridi, Shan Masood, Sohail Khan and Yasir Shah.
NZ Squad:
Kane Williamson (c), Tom Blundell, Trent Boult, Kyle Jamieson, Tom Latham, Daryl Mitchell, Henry Nicholls, Mitchell Santner, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling, Will Young.