The 23-year-old was impressive in the Hammers' 3-0 victory over Fulham, but was forced to withdraw after 67 minutes as a precaution after taking a knock.
Hammers boss Sam Allardyce said afterwards that he does not expect Carroll to recover in time to join up with England squad.
Allardyce told Sky Sports News: "It's a huge result but the only real disappointment for us is Andy might have tweaked a hamstring.
"It is hugely disappointing if that's the case, but it will be unlikely he goes [away with England].
"I don't think he's much chance, sadly for Roy Hodgson and sadly for us. It depends on the extent of the damage."
England travel to Moldova next weekend before playing Ukraine at Wembley as they begin the road to qualification for the 2014 World Cup in Brazil.