New general manager national selection Bruce Edgar says the Northern Knights pair of Sodhi and Anderson have impressed on the current New Zealand A tour of India and will be match ready for the sub-continent conditions.
"Essentially this squad builds on the team that toured England in May. The key was to take a consistent approach to selection and provide continuity for the players," said Edgar.
Knights' bowlers Vettori and Southee were not considered for the tour due to injury. Southee, who had an ankle operation in July, may join the squad when he recovers fully from the injury.
Head coach Mike Hesson says the selection of Sodhi and Anderson will give the side plenty of options on the test pitches in Chittagong and Dhaka.
"Both players have been on our radar and we've been pleased with the consistency Ish showed with the ball on the current NZA tour while Corey made an impressive century earlier this week. Corey gives the squad options as he can bat in the top six and provide useful seam bowling.
"The Bangladesh tour is a good opportunity to introduce a promising spinner, and having two specialist spinners in the squad gives us the option to utilise wickets that are likely to turn."
Sodhi, 20, has come through New Zealand Cricket's age group programme and showed promise at last year's ICC U19 World Cup. He then went on to establish his spot in the Northern Knights and had success in the Plunket Shield.
Anderson made his debut for the Black Caps in the Twenty20 series in South Africa last year and made an impressive ODI debut in the recent Champions Trophy in the UK. The 22-year-old scored a century for NZA against India A on Monday.