Roy Hodgson's side face Moldova on Friday before travelling to Kiev to play Ukraine on September 10, but the trio will not be part of the group.
Cardiff City's Steven Caulker has been called up to the squad to provide defensive cover.
Rooney missed Manchester United's 1-0 defeat to Liverpool on Sunday with a head injury sustained in training, and United boss David Moyes admitted before the game that he was unlikely to feature for the national side.
Jones and Johnson both started the match but limped out with ankle injuries.
Hodgson was at Anfield to watch the game and his fears were realised late on Sunday as their withdrawals were announced.
Caulker - who has one cap - has started every game for Cardiff after his £8million move from Tottenham during the close-season.
England sit second in Group H, two points behind Montenegro but with a game in hand.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
