Shaheen Shah Afridi clean-bowled debutant Tim Robinson for a duck and New Zealand were 1-2 after just two balls before rain denied further play in a reduced five-overs-a-side game.
The toss was delayed for half an hour because of light drizzle in Rawalpindi, and just when Afridi was due to bowl the first ball, rain held up play for more than two hours.
The teams will return for the second T20 of five on Saturday.
Amir and allrounder Imad Wasim came out of retirements and made themselves available for the T20 World Cup in the Caribbean and United States in June, and the Pakistan selectors named them in the 17-man squad for the five-match home series against New Zealand.
Imad wasn't picked to play but Amir was in his hometown for his first international in four years.
New Zealand are without nine key players who have been playing in the Indian Premier League, and the squad was further depleted just before the tour when Finn Allen and Adam Milne were injured in training.Â
New Zealand did award a T20 debut to Robinson, who scored 298 runs at an impressive strike rate of 187.42 in the Super Smash back home.
Rawalpindi will also host the third game on Sunday, and the series will move to Lahore for the last two games on April 25 and 27.
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