Morgan suffered his injury while fielding for Middlesex during their Royal London One-Day Cup match at Somerset on Sunday and will also miss his county's fixtures against Hampshire and Surrey this week.
England internationals Sam Curran and Tymal Mills have also been added to the squad, increasing the roster to 14 members.
England and Wales Cricket Board (ECB) selectors on Wednesday named their one-day worldwide squads to play Scotland and Australia next month, with injured skipper Eoin Morgan included in the playing group despite fracturing his finger playing for Middlesex at the weekend.
"I have a small fracture in the ring finger of my right hand", Morgan explained. However, in the recent development, Morgan ruled himself out of the match due to a broken finger and ICC has named Shahid Afridi as the captain of the World XI.
It is learnt that Morgan fractured his fingers during Middlesex's game against Somerset at Taunton.
He said: "It's not a huge concern, it's one that hopefully we can manage past about a week when the swelling goes down".
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With Morgan out of action, it remains to be seen whether he will be fit to captain England in a one-off ODI against England in Edinburgh on June 10.
Sam Billings is Buttler's replacement for the opening match but is not part of the selection to face Australia.
The 26-year-oldwicketkeeper-batsman has played 13 one-dayers and 17 Twenty20 Internationals, and 142 T20s overall.
The exhibition match is scheduled on May 31 at Lord's, to raise funds for the damages incurred due to the Carribean islands.
The Scotland clash is followed by five ODIs against Australia next month. The match is being organized to raise funds for stadia in the Caribbean that were badly damaged following Hurricanes Irma and Maria past year, the International Cricket Council (ICC) said in a statement.
Andy Flower, the England and Wales Cricket Board s stand-in director, said on the ICC s official website: "It is not a bad crack but it is bad enough to keep him out of tomorrow s Middlesex game and the World XI game".