"After almost three years without missing a Test match, I've now picked up three irritating niggles in the space of seven months and the back spasm that has ruled me out of the Lord's Test is the most annoying of all," Hoggard told The Times.
Right-arm medium pace bowler Hoggard first felt a twinge in his back playing for Yorkshire at Old Trafford last week and suffered some stiffness practising at Lord's on Tuesday.
During a fitness test the following day he "realised straight away that I wouldn't be playing in the Test match", he added in his column in The Times newspaper on Thursday.
Hoggard had an MRI scan on Wednesday before returning to Yorkshire where he will await the results.
England are already without experienced pace bowlers Andrew Flintoff and Steve Harmison because of injury.
Hoggard had been expected to lead a raw bowling attack, with Chris Tremlett and Stuart Broad, yet to make their debuts, in the 13-man squad.
