The 31-year-old Barry, who has played 53 times for England, had a scan earlier on Monday which confirmed that he tore a muscle in his lower abdomen during Saturday's 1-0 friendly win over Norway in Oslo.
Hodgson told the FA website: "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.
"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."
Jagielka, 29, has played 11 times for England and is usually a centre-back. The more versatile Phil Jones has been picked as a defender but could be used in midfield.
Jagielka's call-up dashed the hopes of Liverpool's Jordan Henderson, who had been the midfielder on Hodgson's standby list.
The 23-man squad meet up at the team hotel north of London on Tuesday to resume training ahead of Saturday's friendly against Belgium at Wembley.
The deadline for the 16 finalists to submit their squads to UEFA is on Tuesday.
England are in Group D and face France in Donetsk on June 11 before taking on Sweden and co-hosts Ukraine.
