New Zealand have instead retained Mitchell Santner in the side as the specialist spinner given the competitive edge he holds with his all-round abilities.
The fact that Patel has not played a first-class game since March also went against him whilst finalising the selection of Santner over him, according to head coach Gary Stead.
“The toughest squad selection was clearly around the spinner. That basically came down to the balance of the side and with the four-strong pace attack going so nicely, we wanted to have a spinning all-rounder as an option for that number seven position," Stead noted.
“It’s really unfortunate for Ajaz, who has overcome his calf-injury, but the all-round ability of Mitchell Santner is our preferred option for this series. The fact Ajaz hasn’t been able to have any game-time in the lead-up was also a concern for the selectors," he added.
Patel made his Test debut against Pakistan two years ago when he bowled a memorable spell in Abu Dhabi to help New Zealand clinch a sensational victory by just four runs. He has so far donned the national jersey in eight Tests, picking up 22 wickets at an average of 33.31.
Meanwhile, Kane Williamson returns to the Test line-up after missing the second Test against West Indies in order to be with his wife for their first child.
Williamson will take over the reins from Tom Latham while the uncapped Devon Conway has been excluded from the side.
Seam-bowling all-rounder Daryl Mitchell remains in the team to occupy the vacant slot left by the injured Colin de Grandhomme.
New Zealand's pace battery boasts the presence of Tim Southee, Trent Boult, Neil Wagner and young Kyle Jamieson, implying no room for Matt Henry.
New Zealand are currently third on the ICC World Test Championship table but can move one place ahead if they sweep the two-match series against Pakistan and India is defeated by Australia.
“We’ve got a very settled and experienced group of players who have done the job in our conditions for a long time – so I know they’ll just be focusing on the task at hand rather than worrying about too much down the line," Stead said.
“Our rise through the Test rankings is a great achievement, but we know the challenge is now to back that up against a quality Pakistan side. It’s really exciting to see so much interest in the Test team and I know both games at Bay Oval and Hagley Oval will be special occasions for all involved.”
The first match will begin on November 26 at Bay Oval in Mount Maunganui, followed by the New Year's Test at Hagley Oval in Christchurch on January 3.
Kane Williamson (capt), Tom Blundell, Trent Boult, Kyle Jamieson, Tom Latham, Daryl Mitchell, Henry Nicholls, Mitchell Santner, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling (wk), Will Young