New Zealand skipper Michael Bracewell won the toss, which had also been delayed by 30 minutes, and opted to bat but no action was possible for two-and-a-half hours.
Umpires Ahsan Raza and Aleem Dar then announced a five-over-a-side game at 10:10 local time (9:10 GMT).
Pakistan paceman Shaheen Shah Afridi conceded two leg-byes to debutant Tim Robinson off the first ball before bowling the batsman with a sharp delivery off the next.
But as soon as the Pakistan fielders started celebrating the wicket, the rain returned to force an abandonment.
Fast bowler Mohammad Amir returned to international cricket after nearly four years, having come out of retirement last month, but his participation was limited to just fielding.
The 32-year-old retired in December 2020 after being dropped from the side but changed his mind last month and decided to restart his career, which had already been stalled by a match-fixing ban in 2010.
Pakistan handed T20I caps to batsman Usman Khan, spinner Abrar Ahmed and all-rounder Muhammad Irfan Khan, while Robinson debuted for New Zealand.
The remaining matches are in Rawalpindi on April 20 and 21 and in Lahore on April 25 and 27.
The series gives a chance to both teams to test their bench strength ahead of the Twenty20 World Cup to be held in June in the United States and the West Indies.
New Zealand are without nine key players, including skipper Kane Williamson, who are playing in the ongoing Indian Premier League.
