Barry, 31, was forced off less than 30 minutes after he was introduced as a half-time substitute in Saturday's 1-0 win over Norway and a scan has revealed that the Manchester City midfielder will not travel to Poland and Ukraine.
"I’m very disappointed to lose Gareth, not only was he a member of my original 23-man squad but he has featured prominently in the England team over the last few years," boss Roy Hodgson said in the FA's statement.
"I know how much he wanted to be part of the tournament but I’m sure he will still have a part to play with England after the Euros. I wish him a speedy recovery."
Everton centre-back Jagielka, who can also play full-back and as a defensive midfielder, started against Norway and is a logical call-up with Hodgson naming Glen Johnson as his only specialist right-back in his squad.
Jagielka, 29, also impressed in England's recent friendly victory against Spain and has previously forged a partnership with Manchester City defender Joleon Lescott from their time at the Toffees.
The deadline for submitting final squads for the tournament is 11am on Tuesday.
England's next match is a friendly against Belgium on Saturday.