The Windies will travel to Bangladesh for two Tests, three one-day internationals and three Twenty20 matches in November-December.
Shakib Al Hasan said he was unsure when his second surgery would be conducted as he was yet to fully recover from the infection.
India won the Asia Cup title in Dubai, outlasting Bangladesh by three wickets off the last ball in the final.
Mohammad Amir had a dismal outing in 2018 Asia Cup where he went wicketless in three matches he played in the tournament.
Bangladesh will play against Zimbabwe and the Windies during this three months.
Jasprit Bumrah finished as the second highest wicket-taker in the 2018 Asia Cup.
India defeated Bangladesh on Friday to claim their seventh Asia Cup title
Shikhar Dhawan amassed 342 runs in five matches averaging an impressive 68.80.
Rohit Sharma said that he learned the tricks of the trade from the World Cup-winning captain MS Dhoni.
Under Rohit Sharma, India have won two close multi-nation tournaments.
India defeated Bangladesh by three wickets in a nail-biting contest to lift the Asia Cup title for the seventh time in the history of the tournament.
Ravindra Jadeja starred with both bat and ball in the Asia Cup final against Bangladesh.
Rohit Sharma praised his players for handling the pressure well.
India beat Bangladesh by 3 wickets in the final to retain the Asia Cup title.
MS Dhoni is is now third in the list for the most number of dismissals in Tests, ODIs, and T20Is combined.
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.
Highlights, Asia Cup 2018 Final, India vs Bangladesh (IND vs BAN) ODI Cricket Match: India defeated Bangladesh to clinch their seventh Asia Cup title
Highlights, Asia Cup 2018 Final, India vs Bangladesh (IND vs BAN) ODI Cricket Match: India defeated Bangladesh to retain the Asia Cup title.