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.
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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.
England midfielder Frank Lampard has described the absence of Terry as "a big blow".
The defender's Chelsea team-mate said: "He is a top player and he is experienced at playing these qualifying games. It is a big blow.
"We are blessed with fantastic back-up, whoever comes in. We need someone in the squad to step up and I am sure they will do just that."
England beat Ukraine 1-0 at last summer's European Championship, but Lampard has warned against complacency .
"Ukraine is potentially a tricky game," he continued. "There is talent in their team and they will come here with a desire to beat us but we need to be on the ball.
"It is the early stages, it's a very important game, they have the potential to be up there and in the mix.
"It is a tough game for us, they have some technically very good players and are very organised, they will bring another tough game to the table."
Lampard scored his 25th goal for his country on Friday leaving the Chelsea man one goal behind his countries most prolific international goalscoring midfielders, Bryan Robson and David Platt.
"They are two players I grew up watching," he added. "Robson is a player that gave his all to England and Platt had his goal scoring abilities, that always sticks in my head. Especially that goal against Belgium in the World Cup.
"I'm very proud to be one behind them."