The Football Association has announced that a "minor" problem has forced the left-back to return to Chelsea for treatment.
Cole initially reported to the England team hotel on Monday morning but was given permission to travel back to Cobham to be assessed by Chelsea staff.
Though the vastly-experienced defender will not play against Moldova in Chisnau on Friday, he will return to the England camp on Sunday for further examination.
That means his participation in the second qualifier, against Ukraine at Wembley on September 11, remains uncertain.
Liverpool striker Andy Carroll, currently on loan at West Ham, has been ruled out of both matches with a hamstring injury.
Manager Roy Hodgson has opted not to call up a replacement.