Cook, who does not play the T20 format for England, will not be part of the squad to the Caribbean during which the visitors will play three ODIs and three T20 matches, starting February 28.
Asked if he would be captain against the West Indies, Cook told Sky Sports: "No I won't be. 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 (Stuart Broad) and Gilo (Ashley Giles) time, to really have six weeks together to build for Bangladesh."
England opener Cook failed to score a fifty in the five matches against Australia after a dismal Ashes series, during which the visitors were whitewashed 5-0.
The 29-year-old had hinted at stepping down as England's ODI skipper after his side lost the limited overs series against Australia but later said he was "desperate" to continue in his role.
England lost the final one-dayer on Sunday in Adelaide to lose the series 4-1.
England's limited-overs coach Ashley Giles said Broad, who leads England in the T20 format, will be promoted by the selectors for the ODIs in West Indies.
"The plan is we are playing three one-day games there but with the T20 World Cup we are probably going to pick a T20 squad which gives us a good preparation time running into Bangladesh," Giles said.
"It's likely that Stuart Broad will captain that side."
Image: Alastair Cook
Photograph: Will Russell/Getty Images
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