The 31-year-old Chelsea centre-back is awaiting trial after pleading not guilty on Wednesday to a charge of racially abusing Queens Park Rangers defender Anton Ferdinand during a Premier League match at Loftus Road in October.
The trial date is set for July 9 - eight days after the end of the European Championship in Poland and Ukraine.
Terry will miss Sunday's Premier League match against Manchester United at Stamford Bridge and a likely meeting with Anton's brother Rio - his long-time partner in the centre of England's defence - because of a knee injury which also ruled him out of Chelsea's match at Swansea City on Tuesday.
Rio Ferdinand, who has also captained England in the past and took over as skipper when Terry lost the captaincy for the first time two years ago, said he did not want to be named as his replacement again.
He said on Twitter on Friday: "I don't want to be England captain after the last episode, just want to concentrate on playing for United and if I make the squad then as ever I'll be delighted."
The FA made their decision on Friday, two days after Terry's trial date was announced following an initial magistrates court hearing. In a statement on its website, the FA said: "Following the decision to adjourn the court case against John Terry to July, The Football Association confirm he will not captain the England team until the allegations against him are resolved.
"The FA Board expected the trial to be concluded prior to the European Championships.
"Further to Wednesday's confirmation that the trial will not take place until after the tournament, the board has discussed the matter in detail and has collectively decided it is in the interests of all parties that John has the responsibilities of captaincy removed at this time.
"This decision has been taken due to the higher profile nature of the England captaincy, on and off the pitch, and the additional demands and requirements expected of the captain leading into and during a tournament."
The FA confirmed he had not been excluded from the squad and that manager Fabio Capello is free to select him for the friendly against the Netherlands at Wembley on February 29 and for the European Championships itself.
FA Chairman David Bernstein spoke to both Terry and Capello to explain the facts to them, the FA said.
"Fabio Capello has not been involved in The FA Board discussions which reached this conclusion, but understands that The FA Board has authority to make this decision," the statement continued.
"This decision in no way infers any suggestion of guilt in relation to the charge made against John Terry," the FA added.
It is the second time that Terry has been stripped of the captaincy of the national team in two years. He has played for England 67 times, 34 of them as captain and scored six goals.
He was first relieved of the armband by England manager Capello in February 2010 following allegations of an extra-marital affair, and reinstated as captain last year.
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