England head coach Roy Hodgson appeared to have the luxury of a fully-fit 23-man squad going into the two Wembley matches.
But Cleverley complained of a sore calf after training on Thursday and a scan confirmed he has a problem after he was assessed by the medical team.
He has now returned to his club for further assessment and treatment.
Cleverley did not start England's last Group H qualifier against Ukraine but came off the bench to replace Theo Walcott three minutes from time in the 0-0 draw in Kiev.
Jack Wilshere could be left on the substitutes' bench for tonight's game with Montenegro.
The Arsenal midfielder has been suffering from a cold this week and manager Roy Hodgson could opt for a central midfield of Frank Lampard and Steven Gerrard as his side bids to consolidate their lead at the top of the group ahead of the final qualifier against Poland next Tuesday.
Hodgson was coy on what his first XI will be at Thursday's press conference but Leighton Baines should win his 20th cap at left-back in place of the injured Ashley Cole, while Phil Jagielka and Gary Cahill continue their partnership at centre-half.
Danny Welbeck, Wayne Rooney and Daniel Sturridge could all start, with Welbeck operating on the left and James Milner likely to come in on the right, although Andros Townsend will hope to make his debut from the bench.
Montenegro will be forced to name a weakened side with captain Mirko Vucinic, centre-back Marko Basa and midfielder Miodrag Pekovic all ruled out through injury.
Defender Miodrag Dzudovic is also doubtful for the visitors, who earned a 1-1 draw in the reverse fixture in March.
But Manchester City forward Stevan Jovetic is available to play up front despite recent fitness concerns because of a lack of playing time with his club.