Carroll fell awkwardly after colliding with Fulham centre-back Brede Hangeland midway through the second half of West Ham's 3-0 Premier League win at Upton Park.
The pony-tailed front-man, who joined the London club on a season-long loan from Liverpool on Thursday, immediately clutched his right hamstring and was substituted.
The Football Association said on its website that Carroll was ruled out of the England matches, adding that any decision to replace him would "not be made until after the three league fixtures on Sunday have been completed".
Carroll made an instant impact for West Ham, flicking on a long ball inside the first minute which led to Kevin Nolan's opening goal.
"He will probably be on our treatment bench for a while. He was injured in a jump with their centre-half and he over-extended himself," West Ham manager Sam Allardyce told the BBC.
