The Dublin-born left-hander saw a specialist on Friday about the injury to his right shoulder and will now have an operation next week which will rule him out of all cricket for around three months.
England, who are currently playing a five-match one-day series against India at home, are due to play a series of return fixtures including five ODIs and one Twenty20 starting in October.
"We have will manage the injury with a conservative program but Eoin has now reached the stage where surgery is most appropriate progression of his treatment," ECB medical officer Nick Peirce said in a statement.
"Following the operation Eoin will undertake a rehabilitation programme ruling him out of all cricket for approximately 12 weeks.
"The recovery period is anticipated to see him return to full fitness ahead of England's tour of the UAE commencing in January."
Morgan, who is England's Twenty20 vice-captain, led England to victory against his native Ireland in a one-off ODI last month.
