Cook confirmed that he will not be part of the side which will play three one-day matches against the West Indies from Feb 28 to March 5.
The decision comes on the heels of a 1-4 series defeat to Australia after losing the final match by five runs Sunday.
Cook, who also oversaw an Ashes whitewash, has expressed doubts about his future as captain of England.
However, he told Sky Sports that for tactical reasons he would be giving the Caribbean tour a miss in order for Twenty20 captain Stuart Broad and limited-overs coach Ashley Giles to hone their preparations for the Bangladesh tournament.
"The Twenty20 guys have got their World Cup in Bangladesh and I think we see it as a great six weeks for them to start building the team.
"They're never together very often and it gives them, and Broady and 'Gilo' time, to really have six weeks together to build for Bangladesh."
England and the West Indies will also play three T20 internationals March 9-13.
"We are probably going to pick mainly a T20 squad leading up to Bangladesh so it's likely Stuart Broad will captain," said Giles.