Stuart Broad has been diagnosed with a torn shoulder muscle after being injured during the fourth one-day international against India on Sunday.
He is out of the final ODI on Friday, the Twenty20 series against West Indies and the ODIs in India next month.
England's T20 team is already without Broad's deputy Eoin Morgan because of impending shoulder surgery.
However, one-day captain Alastair Cook has said he would welcome the opportunity to stand in.
"Obviously it's very disappointing for Stuart to miss out," Cook said.
"It's gutting for him, but it gives another person a chance to captain England. The selectors will make that decision.
"It's not whether you'd like the job, it's whether you're honoured enough to be given it."
Broad initially revealed the injury news on his Twitter page writing: "Bad news on the shoulder: torn a muscle. Gutted."
England and Wales Cricket Board chief medical officer Dr Nick Peirce said: "Exact timescales will be determined in due course but he is likely to be ruled out of cricket for a number of weeks.
"Stuart has a muscle tear within his shoulder and will require an initial period of rest and rehabilitation."