The 32-year-old Bennett has not played for New Zealand since a one-day international against Bangladesh in 2017. He has yet to play a Twenty20 international.
Boult (hand), Henry (thumb) and Ferguson (calf) were all injured in New Zealand's 3-0 test series loss to Australia.
"We're delighted to have Hamish back in the fold for what will be a huge series against India," selector Gavin Larsen said in a statement on Thursday.
"We all know he brings good pace and bounce but it's the clever variations he's added that make him such a well-rounded T20 bowler."
Captain Kane Williamson returns to the Twenty20 squad after he missed the series against England in November because of a hip injury while batsman Tom Bruce and all-rounder Colin de Grandhomme will share the series.
De Grandhomme will play the first two games in Auckland and third in Hamilton, with Bruce available for the matches in Wellington and Mt. Maunganui.
All-rounder Jimmy Neesham, who suffered a thigh injury in domestic Twenty20 matches, has also missed out on the squad but has been named in a New Zealand A side to play India A in three one-day matches.
The first match of the Twenty20 series is at Eden Park on Jan. 24, with the final game in Mt. Maunganui on Feb. 2 before a three-match one-day series and two tests.
New Zealand Twenty20 squad: Kane Williamson (captain), Hamish Bennett, Tom Bruce (games 4-5), Colin de Grandhomme (games 1-3), Martin Guptill, Scott Kuggeleijn, Daryl Mitchell, Colin Munro, Ross Taylor, Blair Tickner, Mitchell Santner, Tim Seifert, Ish Sodhi, Tim Southee.
(Reporting by Greg Stutchbury; Editing by Ed Osmond)