The 23-year-old Siraj, a pace bowler for Indian Premier League (IPL) side Sunrisers Hyderabad, was called up after a string of impressive performances for India A.
Iyer is a 22-year-old right-handed batsman who plays first-class cricket for Mumbai. He has turned out for the Delhi Daredevils in the IPL.
The T20I series follows a three-match ODI contest between the sides.
New Zealand stunned the hosts in the first 50-over match on Sunday, successfully chasing down 281 thanks to an unbeaten Tom Latham century and 95 from Ross Taylor.
A Virat Kohli ton had fired India to 280-8 but New Zealand won the match by six wickets and with six balls to spare, finishing on 284-4.
The first T20I takes place in Delhi on November 1. The teams will then line up in Rajkot on November 4 followed by the final match in Thiruvananthapuram on November 7.
Veteran bowler Ashish Nehra, who is due to retire after the first match, will drop out of the squad for the remaining fixtures, selectors said in a statement.
India’s squad
Virat Kohli (c), Mahendra Singh Dhoni (wk), Shikhar Dhawan, Rohit Sharma, Lokesh Rahul, Manish Pandey, Shreyas Iyer, Dinesh Karthik, Hardik Pandya, Axar Patel, Yuzvendra Chahal, Kuldeep Yadav, Bhuvaneshwar Kumar, Jasprit Bumrah, Ashish Nehra, Mohammed Siraj
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