Williamson, Anton Devcich, Roneel Hira and Trent Boult have been included in addition to those players who represented New Zealand in the format against the West Indies.
Ryder wasn't considered after his recent off-field behaviour issues.
"That created a gap," said Bruce Edgar, the NZC general manager of national selection.
"Mike [Coach Hesson] and I were not happy with his preparation [for the first India test] and we've had to exclude him. Character's really important to us as part of the selection process. If we feel there's form and skill but a player's character doesn't stack up, we'll consider not selecting them."
Adam Milne (abdominal strain) and Matt Henry (adductor strain) also weren't considered.
"They form part of a bigger picture. We don't want to rush them back to a point where they get injured again," Edgar said.
The addition of Williamson, Devcich and Hira reflects the selectors' desire to focus on those capable of benefiting from the spin-friendly conditions expected.
"On previous tours of Bangladesh a lot of spin has been bowled at us so we've got to bowl a lot of spin back at their guys. Those three give us that option," Edgar said.
Williamson and Devcich double as opening options.
"Kane's ODI game has recently developed to another level against India. His success on the sub-continent and ability to play spin bowling has also always been good. We're going to get spin, even at the top of the order.
"Anton also gives us a spin and top order option. He bats at a good strike rate, bowls handy left-armers and is an excellent fielder. We see this as a continuation of his development. He's played well in the HRV Cup and performed well on the tour to Bangladesh and the New Zealand 'A' tour to India and Sri Lanka before that."
Boult will be introduced as a way of pushing him to play more in the limited overs formats.
"Trent is a high quality player. We tried to get him into the ODIs against India but he had a quad strain. We feel confident of bringing him in here for an opportunity."
The squad departs for a pre-tournament camp in Abu Dhabi on March 8 where they'll play warm-up matches against Worcestershire. Once in Bangladesh, the team will have official tournament warm-up matches against Pakistan (March 17) and Australia (March 19).
New Zealand matches at the ICC World Twenty20 in Bangladesh:
March 23 v England, Chittagong
March 24 v South Africa, Chittagong
March 29 v qualifier, Chittagong
April 1 v Sri Lanka, Chittagong
Followed by semi-finals and finals depending on group play results.
New Zealand squad for ICC World Twenty20 in Bangladesh:
Brendon McCullum (c) - Otago
Corey Anderson - Northern Districts
Trent Boult - Northern Districts
Anton Devcich - Northern Districts
Martin Guptill - Auckland
Roneel Hira - Canterbury
Mitchell McClenaghan - Auckland
Nathan McCullum - Otago
Kyle Mills - Auckland
Colin Munro - Auckland
James Neesham - Otago
Luke Ronchi - Wellington
Tim Southee - Northern Districts
Ross Taylor - Central Districts
Kane Williamson - Northern Districts
