The 24-year-old is to return to Liverpool for treatment on a thigh injury and will miss England's qualifier at Wembley on Friday but may be fit to face Ukraine on Tuesday
Although the forward returns to his club for treatment, he has not been ruled out of the Three Lions' match in Ukraine on Tuesday.
Sturridge has scored three goals in the Reds' first three matches of the Premier League season but revealed in the aftermath of Sunday's 1-0 win over Manchester United that he was struggling with a leg injury.
An FA statement read: "As Roy Hodgson prepares his England team to face Moldova on Friday evening, Daniel Sturridge has returned to Liverpool for further treatment.
"The squad departed St George's Park on Thursday afternoon ahead of the World Cup qualifier at Wembley but the Liverpool forward will return to his club with the intention of joining the England squad again at the weekend and travelling to Ukraine."
Hodgson is already without Wayne Rooney, who sustained a gash to his forehead while training for Manchester United, leaving the 65-year-old with limited options up front for two crucial qualifiers.
England are just one point ahead of third-place Ukraine in Group H but have a game in hand over leaders Montenegro, who sit two points clear at the summit.