Terry suffered the setback during Friday night's 5-0 win in Moldova and England finished the game with 10 men after the Chelsea defender limped out of the action in the closing stages.
He continued to have treatment on Saturday after returning to England but it has been decided, an FA spokesman said, that Terry will not recover sufficiently in time to face the Ukrainians.
Gary Cahill is likely to replace Terry and partner Joleon Lescott at centre-back in the second qualifying match of the campaign.
It would be Cahill's first appearance at Wembley since he suffered the broken jaw against Belgium which ruled him out of Euro 2012.
Phil Jagielka, who partnered Lescott when they were team-mates at Everton, is the other player in contention.
Terry was one of England's most consistent performers at the European Championship and helped his country overcome Ukraine in a group encounter.
Left-back Ashley Cole had already been ruled out with the ankle injury which prevented him from playing in Chisinau and remains on 98 caps.
But Leighton Baines proved a capable deputy against Moldova and scored England's final goal.
- Joleon Lescott