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The side will be captained by Tim Southee with Kane Williamson, who has sat out the ODI series with an elbow injury, given a break before heading to the IPL along with Trent Boult, Mitchell Santner, Kyle Jamieson, Jimmy Neesham and Tim Seifert.
Allen (Royal Challengers Bangalore), Milne (Mumbai Indians) and Ferguson (Kolkata Knight Riders) will head to India straight after the conclusion of the series against Bangladesh.
The 21-year-old Allen has been one of the breakout stars of the domestic season where he plundered 512 runs in the Super Smash for Wellington
"It's especially an exciting time for Finn, who will be getting his first taste of the Black Caps environment," selector Gavin Larsen said. "His Super Smash campaign with the Firebirds was nothing short of outstanding and we believe he has the skills to succeed at the next level.
"We're delighted to see Lockie and Adam return after working really hard to get back to this point. They are two of the premier fast bowlers in world cricket and it's fantastic to be able to call on their services, in what is shaping as a big year of T20 cricket.
In Seifert's absence, Devon Conway will take the wicketkeeping gloves. There are two legspinners in the squad with Todd Astle joining Ish Sodhi.
"It's certainly been a season like no other and once again we've had to be pragmatic in our approach," Larsen said. "The six guys who will miss this series are incumbents in our T20 side and the decision to give them some time at home with family before they embark on a long stint in India, was principally made with their welfare in mind.
"We're also very aware of the need to give others opportunities in a World Cup year and it's great to be able to introduce Finn and Will to the set-up, as well as welcome back Lockie and Adam.
"Tim's a great leader in any Black Caps side, we've seen how well he's slipped into the T20 captain's position in the past and we look forward to him continuing to grow in the role.
"Devon's wicketkeeping skills are a real asset to have in a squad and we're keen to ensure he has some international experience in this role to provide us with another option going forward."