The Football Association confirmed the news on Monday evening when they also announced that Arsenal's Kieran Gibbs had been called into the squad as a replacement.
The news means Everton's Leighton Baines is likely to start the game at left-back.
Cole complained of a rib problem during Chelsea's Premier League victory at Norwich on Sunday and underwent a scan on Monday.
It is not yet known whether Cole, who will return to Chelsea for treatment on his injury, will be available for next Tuesday's clash with Poland, also at Wembley.
England need to win both games to guarantee their place at next summer's finals in Brazil.
Cole has a wealth of experience at international level having won more than 100 caps and played in three World Cups.