Terry is the third player to withdraw from the game after Aaron Lennon and Phil Jagielka were forced out with back and hamstring injuries respectively.
Aston Villa's Stewart Downing and Gary Cahill of Bolton have already been drafted into the squad as replacements.
England coach Fabio Capello will name his captain at lunchtime on Monday.
The Italian is to announce his decision in a press conference after training at Wembley, with Rio Ferdinand and Steven Gerrard the two men in contention.
Capello turned to Ferdinand after stripping Terry of the armband in February following newspaper allegations about his private life.
Young seeks starting spot
But when the Manchester United defender suffered a back injury playing for his club, Liverpool midfielder Gerrard was asked to step into the breach.
Ferdinand returned to lead the side in World Cup warm-up matches against Mexico and Japan, only to be ruled out of the tournament after damaging knee ligaments in training.
Gerrard filled in for all four of England's matches in South Africa, August's friendly against Hungary and their opening two Euro 2012 qualifiers, but Ferdinand has since regained fitness and form.
The absence of Terry and Jagielka means Capello will name a different central defensive pairing for the fifth consecutive game, with Ferdinand set to start alongside either Cahill or Manchester City's Joleon Lescott.
"Terry was assessed by England medical staff on Sunday and will not be fit to play any part in Tuesday's game," said a Football Association statement.
For Terry, 29, the back problem is the return of an injury that he had an operation to cure in 2006.
Ferdinand has played only four times since returning from his knee injury, although Lescott performed admirably alongside Jagielka in last month's victory over Switzerland in Basle.
While Terry is notorious for shrugging off minor problems, he was forced out of the double-header against Bulgaria and Switzerland with a hamstring injury.
It will mean he has only featured once for his country since the World Cup.
The injury will also be a concern for Terry's club manager Carlo Ancelotti who has Alex and Yossi Benayoun ruled out since the Blues were last in action against Arsenal a week ago.
Tottenham winger Lennon missed training on Friday after reporting the problem and after further tests on Saturday morning, it was decided to send him back to his club for further treatment.
Bent hints at two-man attack
Jagielka produced two towering central defensive performances in last month's wins and the Everton player had been expected to retain his place.
But the 28-year-old missed a training game at Arsenal's London Colney complex on Friday after experiencing some tightness in his hamstring. He then underwent a scan which confirmed he would not be fit in time for Tuesday's match.
Meanwhile, Manchester City midfielder Gareth Barry joined up with the squad on Friday after being given additional time at home because of personal reasons.
Arsenal midfielder Jack Wilshere has joined the senior players for the match against the Group G leaders after playing for the under-21s as they beat Romania 2-1 in the first leg of their Euro 2011 play-off on Friday.
England Under-21 manager Stuart Pearce was hoping to have Wilshere available for the second leg on Tuesday but is delighted that the Arsenal youngster is getting his senior chance.
"Part of me is pleased that he is going, as it shows to the rest of the squad the pathway which is there for the players, part of me would have liked to have him in Romania," said Pearce.
"I also hope Jack gets a game against Montenegro.
"With his form for club and country, he deserves to be with the seniors and good luck to him."
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