Tamim was plagued by woeful form during the World Cup and failed to deliver in the three-match ODI series in Sri Lanka, where he fulfilled the captaincy responsibilities in the absence of Mashrafe Mortaza.
He thus requested a short break from international duties to recover his mental and physical strength.
Meanwhile, the selectors have recalled Arafat Sunny and Al-Amin Hossain into the side, both of whom last appeared in a T20I match three years ago.
The 33-year-old Sunny was suspended for an illegal bowling action detected during the 2016 World T20 in India.
He later had a run-in with the law when he was arrested in 2017 for posting offensive photographs of his girlfriend on social media.
With Taijul Islam left out of the T20I squad, Sunny's inclusion seems a like-for-like replacement for the left-arm off-spinner.
"We have recalled Sunny because we need someone experienced for India, which is a tough country," chief selector Minhajul Abedin told reporters.
Paceman Al-Amin will bolster the fast bowling department with Mohammad Saifuddin, Mustafizur Rahman and Shafiul Islam already in the lineup.
"Al-Amin comes into the squad as some of our other fast bowlers are injured," Abedin admitted, as he recently showed concern over Mustafizur's fitness.
Soumya Sarkar, who was dropped from the side midway through the previous series, has made a comeback.
Sabbir Rahman, Najmul Hossain and Rubel Hossain are the other individuals discarded from the team.
Bangladesh have never won a T20I game against India – a record they would be hoping to better when the two sides meet for the first of three matches on November 3 in New Delhi.
Shakib Al Hasan (c), Tamim Iqbal, Liton Das, Soumya Sarkar, Naim Sheikh, Mushfiqur Rahhim, Mahmudullah Riyad, Afif Hossain, Mosaddek Hossain, Aminul Islam Biplob, Arafat Sunny, Mohammad Saifuddin, Al-Amin Hossain, Mustafizur Rahman, Shafiul Islam