The Boxing Day Test is scheduled to be played in Mount Maunganui from December 26-30.
While Babar has fractured his right thumb, Imam has injured his left thumb during training sessions in Queenstown last week.
According to a statement issued by the Pakistan Cricket Board, both the batsmen are yet to return to the nets and the team's medical staff was closely monitoring their progress.
"Decision on their participation in the second Test, which commences in Christchurch on 3 January, will be made closer to the time," the PCB said.
In Babar's absence, wicketkeeper Mohammad Rizwan will lead Pakistan in the first Test and will become his country's 33rd Test captain.
The duo's absence proved to be lucky for prolific domestic run-scorer Butt, who is expected to make his Test debut on Saturday.
Balochistan's 24-year-old Butt scored 191 runs in three four-day first-class Quaid-e-Azam Trophy matches before joining the New Zealand-bound tour party.
He had topped the batting charts in the 2019-20 Quaid-e-Azam Trophy with 934 runs at an average of over 62 and four centuries.
Also returning to the Pakistan Test side are Abid Ali, Azhar Ali, Fawad Alam, Haris Sohail, Mohammad Abbas, Naseem Shah, Shan Masood, Sohail Khan and Yasir Shah.
They will replace Abdullah Shafiq, Haider Ali, Haris Rauf, Hussain Talat, Iftikhar Ahmed, Khushdil Shah, Mohammad Hasnain, Musa Khan, Usman Qadir and Wahab Riaz, who will now join Pakistan Shaheens (A team) for five T20 matches against the local and New Zealand XI sides.
The PCB further said that Imad Wasim and Mohammad Hafeez will no longer be seen in action on the New Zealand tour. While Imad will travel to Australia to join Melbourne Renegades in the BBL, Hafeez will return to Pakistan.
Pakistan started their tour on a disappointing note, handing New Zealand an unassailable 2-0 lead in the three-match T20 series. The final T20 will be played here before the focus shifts to the two-Test rubber.
"It is disappointing to lose the T20I series against a well-settled New Zealand side, who utilised their resources and conditions to their advantage.
"We need to up skill and improve our individual and team performances, including in Tuesday's match, and the sooner we get these sorted the better it will be for us," Pakistan's head coach Misbah-ul-Haq said.
Pakistan squad for Tests: Mohammad Rizwan (captain for 1st Test), 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. (Babar Azam and Imam-ul-Haq not available for first Test).
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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