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 25-year-old has suffered several injuries since moving to Anfield in January 2013, and Liverpool boss Brendan Rodgers will be hoping his latest problem will not keep him on the sidelines for long.
The FA have not revealed whether Hodgson will call-up a replacement in the absence of Sturridge.
