The Chelsea defender has a "minor ankle concern" and will be unavailable for Friday's World Cup qualifier, but could return to feature in next week's clash with Ukraine
The 31-year-old has returned to his club in order to receive further treatment on the knock which is described as "minor" by the FA's official website.
Three Lions boss Roy Hodgson remains hopeful that the left-back could make a return in order to feature in the second qualifying clash next Tuesday against Ukraine.
Cole, who helped Chelsea to their maiden Champions League success last term, featured in every game at Euro 2012 as England were knocked out by Italy at the quarter-final stage.
The upcoming games mark Hodgson's first qualifiers with England after he succeeded Fabio Capello in the national team hotseat with a European Championships place already confirmed.
England's meeting with Moldova in Chisinau will kick off at 19:45BST on Friday.