The Old Trafford club said Fletcher had "accepted medical advice to take an extended break".
He is taking a rest "in order to afford the best chance possible of achieving full remission once again".
“He is one of the most inspirational players I have had the pleasure of working with and, on behalf of his Scotland team-mates and my backroom staff, I sincerely hope this time off, allied to the support of his family, will enable him to make a full recovery”
Scotland manager Craig Levein
The statement added: "Darren's continued desire to play and his loyalty to both club and country has probably compromised the chances of optimising his own health and fitness.
"We request that his privacy is respected and hope that the removal of the additional stress associated with speculation regarding his health will also aid his recovery."
Fletcher signed a new four-year deal until 2015 with United in March.
Fletcher made only one start for United last term after 1 March and was an unused substitute for the 3-1 Champions League final defeat by Barcelona. He has made 10 appearances in all competitions for United during the current campaign.
Fletcher's absence is another blow to United, who suffered a huge setback last week when they were eliminated from the Champions League in the group stage for only the third time in 16 years.
It is also a big loss for Scotland, for whom Fletcher is an integral figure. Their next match is a friendly against Slovenia in February.
Man Utd appearances:
Man Utd goals:
4 Premier League titles (2007, 2008, 2009, 2011), 1 FA Cup (2004), 2 League Cups (2006, 2010), 1 Champions League (2008), 1 World Club Cup (2008)
v Basel, 12 March, 2003 (Champions League second group stage)
Most recent game:
v Benfica, 22 November, 2011 (Champions League group stage)
Fletcher's last appearance in international football came in November's
2-1 friendly win for Scotland in Cyprus
. He played for 64 minutes before being replaced by Brighton's Craig Mackail-Smith.
Scotland manager Craig Levein said: "I am obviously absolutely devastated for Darren because I know how hard he has worked to get back to playing regularly for his club and country.
"He is one of the most inspirational players I have had the pleasure of working with and, on behalf of his Scotland team-mates and my backroom staff, I sincerely hope this time off, allied to the support of his family, will enable him to make a full recovery."
Levein hailed Fletcher's on-pitch efforts, adding: "Darren has shown tremendous dedication and fortitude, demonstrated by his ability to overcome this illness and perform at the highest level for Manchester United and Scotland.
"I spoke with Sir Alex Ferguson and Darren this week and the most important thing, at this stage, is for the player to be given time to rest and recuperate. Nobody is more committed to his country's cause than our captain.
"He is a central part of our plans for the World Cup 2014 qualifiers but, at this stage, his health is paramount and I would like to reiterate the best wishes of everyone at involved with the national team and the Scottish FA."
Fletcher's illness, which also afflicts five-time Olympic gold medallist Sir Steve Redgrave and former England rugby union captain Lewis Moody, could result in surgery, according to a leading medical specialist.
"Most patients experience periods of good health and periods of bad health," Professor Alastair J M Watson, Professor of Medicine and consultant gastroenterologist at Royal Liverpool University, told BBC Sport.
"In most people, it is quite mild and no more than a minor inconvenience, but in a proportion of patients it can be severe.
Archive - Fletcher scores for Scotland
"In some cases, it has to be treated by having the bowel removed, but that is the worst-case scenario.
"It is a disease which gets worse in times of stress so resting along with drugs will help.
"It affects about one in 500 people and if anything is getting more common rather than less common."
Fletcher's absence leaves United manager Sir Alex Ferguson with another selection problem.
The club's only specialist midfielders currently available are Michael Carrick, Park Ji-sung, Darron Gibson and Ryan Giggs, although United have made use of the versatile Phil Jones. Reserve midfielders Paul Pogba and Ravel Morrison are possible options.
United's injured midfielders include Anderson, expected back in February, and Tom Cleverley, who is aiming to return for some Christmas fixtures.
Former Scotland star Pat Nevin said: "It is really bad news but the good thing for Darren is that Manchester United will ensure he gets the best possible treatment and his good health is paramount.
"I watch him regularly for Scotland and they have not just built a team around him as a player, they have built it around his ethics and approach to the game.
"He is honest and incredibly hard-working, so when you examine those qualities it is no surprise he has tried to play through his illness time and time again until he was no longer able to do so."
Manchester United striker Michael Owen said on
: "Wishing Fletch all the best in his recovery. #topbloke."
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