Carrick has been suffering with an Achilles injury, although he did play the full 90 minutes of his side's Premier League victory over Arsenal on Sunday.
His Manchester United teammate Welbeck has been ruled out with a knee problem, having failed to feature for his club since October 19.
"Danny Welbeck and Michael Carrick have both withdrawn from the England squad due to injury," the FA said in a statement on its website. "The Manchester United duo featured in last month's World Cup qualifier against Poland, but are ruled out as Roy Hodgson's men gather for two games at Wembley Stadium."
No replacements have been called up to Hodgson's squad for the fixtures against Chile on Friday and Germany on Tuesday.