The ICC barred Sunny and Taskin from bowling in international cricket on Saturday after their bowling actions were assessed as illegal.
Saqlain and Shuvagata are scheduled to fly for Bengaluru on Saturday night.
While it is a return to the Tigers' fold for Shuvagata, Saqlain has broken into the national team for the first time.
Habibul Bashar, a member of the Bangladesh Cricket Board selection committee, said Saqlain was an obvious selection to replace Sunny.
"Actually Saqlain had been at the doorsteps of the national team for many days. He has done well for the A team recently. Saqlain was our best choice after Sunny," Bashar told bdnews24.com over the phone on Saturday.
The former Bangladesh captain said the selectors went for Shuvagata as a replacement for the pace of Taskin keeping the Indian conditions in sight.
"We had included five pacers in the team with the conditions of Dharamsala in mind. Now we feel maybe the team won't play with more than three pacers considering the forthcoming matches.
"The team management wanted a spinning option, so we went for Shuvagata."
Mashrafe Bin Mortaza and his men lost their Super 10 opener against Pakistan by a big margin on Wednesday at Kolkata's Eden Gardens.
Bangladesh will take on Australia on Monday and India on Wednesday in Bengaluru. The team will return to Kolkata for the last Group 2 match against New Zealand.