Sturridge reported for duty at St George's Park on Sunday evening with the remainder of the squad but was unable to take part in training on Monday morning and returned to his club Liverpool for further treatment.
The 23-year-old was injured during the first half of Liverpool's 2-2 draw at Manchester City, shortly after scoring the Reds' opening goal, but was not substituted until the closing stages of the game.
Sturridge's withdrawal leaves England boss Roy Hodgson with only two fit strikers at this stage - Manchester United duo Wayne Rooney and Danny Welbeck - after Tottenham's Jermain Defoe pulled out with an ankle problem, although Hodgson does also have the option of playing Theo Walcott up front.
Manchester United midfielder Michael Carrick also dropped out on Sunday with a hip injury.
Only 12 England players trained normally on Monday morning as the remainder who were in action on Sunday did a warm-down session instead.