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".
England, already without injured striker Wayne Rooney, open their Group H campaign in Moldova on Friday before hosting Ukraine four days later.
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.
The 23-year-old Carroll moved to London in search of the form that led Liverpool to pay a club record fee of 35 million pounds ($55.59 million) to Newcastle United for him in January 2011.
Carroll failed to live up to that price tag at Anfield, scoring 11 times, and West Ham have the option of signing him on a permanent deal at the end of the season for an undisclosed fee.
- West Ham