Cole ruled out of England clash against Ukraine
Cole, who has won 98 caps, took the knock when his Chelsea side were thumped 4-1 by Atletico Madrid in the European Super Cup match in Monaco last week.
The FA said in a brief statement on their website: "Ashley Cole was assessed by the medical staff on Saturday and will not be available for the qualifier with Ukraine on Tuesday."
The FA also said that Cole's Chelsea team-mate John Terry was having treatment from the medical team after hurting his ankle against Moldova.
England finished the game with 10 men after Terry limped off just before the end.
If Terry does not play his fellow Chelsea defender Gary Cahill is likely to replace him and partner Manchester City's Joleon Lescott in the heart of the defence.
Terry was involved in a highly controversial incident against Ukraine during Euro 2012 when he cleared a shot away from the England goal after the ball had crossed the line.
UEFA, European football's ruling body, have since admitted the goal should have been given, but it was not and England won the match 1-0.