The Liverpool forward has returned to his club for treatment on his left thigh after suffering the injury during his side's 4-2 win over Notts County in the League Cup last Tuesday.
Sturridge was fit enough to feature in Liverpool's 1-0 win over Premier League champions Manchester United on Sunday, but will not be available for selection against Moldova at Wembley
The 24-year-old, however, could feature in Tuesday's qualifier against Ukraine.
A statement on the Football Association website read: "Daniel Sturridge has returned to Liverpool for further treatment.
"The Liverpool forward will return to his club with the intention of joining the England squad again at the weekend and travelling to Ukraine."
England are currently two points behind leaders Montenegro in Group H, having played a game less.
Losing Sturridge is undoubtedly a blow to England manager Roy Hodgson as the striker has scored five goals for Liverpool this season in all competitions.
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