West Indies registered their first victory to stay alive in the series after suffering a five-wicket loss in the opening match on Sunday.
Tamim Iqbal has not played since injuring his wrist during the Asia Cup opener against Sri Lanka in September.
Bangladesh defeated the Windies by an innings and 184 runs to register their first Test series win in four years.
The Windies were reduced to 75 for five at stumps on the the second day, trailing Bangladesh by 433 runs in the first innings.
Bangladesh lead the two-Test series 1-0.
Bangladesh came close to winning series twice in the past two years.
Shakib Al Hasan dismissed Windies opener Kieran Powell on Day 3 to reach the 200-wicket mark in Test cricket.
Riding on Mominul Haque's 120-run knock, Bangladesh scored 315 for eight against the Windies on the opening day of the first Test.
Shakib Al Hasan said he was unsure when his second surgery would be conducted as he was yet to fully recover from the infection.
Bangladesh will play against Zimbabwe and the Windies during this three months.
Shakib Al Hasan had missed the virtual Asia Cup 2018 semi-final against Pakistan after he complained of a fresh pain in an injured finger.
Ravindra Jadeja claimed four wickets in the Super Four match against Bangladesh in the Asia Cup 2018.
Bangladesh are drawn in Pool B with Sri Lanka and Afghanistan in the Asia Cup, scheduled to be held from September 15 to 28.
Bangladesh withstood a withering assault from Andre Russell to complete a series-clinching 19-run victory on the DLS Method over the West Indies in the rain-affected deciding final fixture of their three-match T20 International Series on Sunday.
With the win, Bangladesh kept the series alive and also ended a five-match losing streak in T20Is going back to the final of the tri-nation series against India last March.
Man-of-the-Match Tamim blasted an unbeaten 130, the highest by a Bangladeshi in ODIs against the West Indies, while Shakib weighed in with 97 a second-wicket partnership of 207.
Bangladesh on Wednesday slumped to their lowest-ever Test total as Shakib Al Hasan's team was bowled out for a paltry 43 against the West Indies.
Chasing 146 for victory, Bangladesh required nine in the 20th over but Khan held his nerve to restrict Bangladesh to 144-6 in the north Indian city of Dehradun.