Cole has returned to his club to undergo further treatment on the injury, and will be reassessed by England staff on Sunday to see whether he will be ready to face Ukraine.
The 31-year-old picked up the injury during his side's 4-1 loss to Atletico Madrid in the European Super Cup on Friday.
"After reporting to the England hotel on Monday morning, Ashley Cole has returned to Chelsea for further treatment," read an FA statement.
"Cole has a minor ankle concern and will be treated by his club this week, before being assessed by the England Medical staff on Sunday to see if he is available for the FIFA World Cup qualifier with Ukraine, on Tuesday 11 September."
Cole could have won his 100th cap for his country against Ukraine had he played against Moldova, as he currently sits on 98.