The Liverpool striker limped out of training on Friday and will play no part in the Monday's opening Group E clash in Basle.
A Football Association spokesman said: "Daniel Sturridge picked up an injury on his thigh in training.
"He has had a scan and will now return to Liverpool FC for treatment. He will play no part in the forthcoming Switzerland match."
Sturridge's injury is a major blow to England manager Roy Hodgson, as the former Chelsea forward has emerged as a key man playing alongside captain Wayne Rooney.
The FA have not revealed whether Hodgson will call-up a replacement in the absence of Sturridge.
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