Paes had played in the World Group play-off tie against Serbia in Bangalore, which India lost 2-3 in September last year.
In Paes' absence, seasoned Rohan Bopanna and Saketh Myneni will do the doubles duty in the July 17-19 tie, to be held in Christchurch.
Talented youngster Ramkumar Ramanathan is also in the side as a reserve player.
Speaking to PTI, Selection Committee chairman S P Misra said, "Paes has opted out since he has other commitments. He said he was not available for this tie."
Misra said since it was an away tie, one reserve has been kept in the side. Jeevan Nedunchezhiyan was part of the squad in the Bangalore tie along with Ramkumar.
India coach Zeeshan Ali said, "Paes has not given any specific reason but he said he would be available for the next tie in September."
Zeeshan is of the view that the conditions would be challenging for his side, which would surely start as favourite.
"On paper we appear strong. But we will be playing in 5 to 8 degrees temperature. We are not used to playing in such extreme cold conditions although we will be playing indoors. And they are a different side from the one which travelled to Chandigarh and lost 0-5 (in 2012). Their two players are in top-100 doubles and doing well."
Zeeshan also said that the team will travel to Christchurch one week before the tie.
"We can't go earlier due to Wimbledon," he said.
In the head-to-head record, India have beaten New Zealand four times in seven ties.
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