The Football Association confirmed the news on Tuesday evening, adding that no replacement has been called up by manager Roy Hodgson for the two friendly fixtures.
"Andy Carroll has been ruled out of the England squad for the upcoming internationals with Republic of Ireland and Brazil," an FA statement read.
"Carroll had been named in Roy Hodgson's squad that will take on Ireland at Wembley on Wednesday, May 29, and then travel to Rio to face Brazil on June 2, but has now been forced to withdraw through injury.
"No replacement will be made at this time."
The news is a blow to Hodgson, who had spoken glowingly about Carroll's end-of-season form at loan club West Ham.
There is no obvious alternative to the target man in the remainder of the squad, which includes Manchester United pair Wayne Rooney and Danny Welbeck, plus Liverpool's Daniel Sturridge and Tottenham forward Jermain Defoe.
England's players are due to meet up at St George's Park on Sunday, by which time it should be known whether or not Tom Cleverley will be available.
The Manchester United midfielder suffered a calf injury during the season-ending 5-5 draw at West Brom last weekend.