The 24-year-old complained of a sore calf on Thursday and after a scan, the Football Association have confirmed he has returned to his club for treatment.
"Tom Cleverley has been ruled out for England's two World Cup qualifiers against Montenegro and Poland," said the FA.
"Cleverley complained of a sore calf after training on Thursday afternoon and had a scan later that day.
"Following the results the England medical team confirmed he would miss the upcoming two matches and he has returned to his club for further treatment."
While it appeared unlikely Cleverley was going to start against Montenegro on Friday evening, he would have been a useful option from the bench in that game and against Poland on Tuesday.
He has been one of the most used players under Hodgson, starting every game he was available for under the 66-year-old last season.
United manager David Moyes will be hoping the damage is not too extensive given another midfielder, Marouane Fellaini, is playing through the discomfort of a wrist injury that will eventually require surgery. In addition, Robin van Persie is believed to be suffering a toe injury.