Cole missed Friday night's 5-0 win over Moldova with an ankle problem but Roy Hodgson had hoped the left-back would be fit for Tuesday night's game at Wembley.
However, Leighton Baines, who scored with a deflected free kick in Chisinau, will make his second competitive start for his country as Cole has not recovered in time.
Terry sustained his injury during the win in Moldova and was eventually forced from the pitch despite England having made all three substitutions.
The defender will receive further treatment before it is determined whether he will be available to face Ukraine.
His Chelsea team-mate Gary Cahill is likely to come in alongside Joleon Lescott if Terry is ruled out.