Carrick injured an ankle in United's 7-1 win over the League of Ireland in Dublin on Wednesday and the problem will also sideline him for the opening matches of the Premier League season.
He was one of a number of injured players highlighted by manager Alex Ferguson at a news briefing on Friday with the United boss adding Rio Ferdinand and midfielder Anderson would also miss the game.
"Anderson is making quite good progress, Rio is still well behind, (Owen) Hargreaves is still in the States, the two Da Silvas (Fabio and Rafael) had food poisoning in the week and are doubtful for Sunday so we are not in a great position. Carrick will be out for a couple of weeks," Ferguson said.
He also said England striker Wayne Rooney and former international front man Michael Owen would play for part of Sunday's match.
"Rooney and Owen definitely need to play 45 minutes on Sunday - and as we have had to do with the Community Shield for the last few years, we'll use it as a mechanism to get players further down the line in terms of fitness."
Cech, who saved two spot-kicks when his side beat United on penalties in last year's Community Shield match, has a calf injury but is expected to be fit by next Saturday when the league and FA Cup double winners kick-off the season with a home match against promoted West Bromwich Albion.
United and Chelsea are meeting in the Community Shield for the third time in the last four seasons with the two previous games both ending in draws. United won on penalties in 2007 and Chelsea did the same last season after a 2-2 draw.
Ferguson's side has won the trophy eight times in his 24-year reign at Old Trafford and he will be keen to maintain United's generally good pre-season form with four wins win in their six matches.
Chelsea, in contrast, have yet to find any form in their warm-up matches, losing three and winning one.
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