The Liverpool striker, 25, suffered a thigh strain in Friday's training session at St George's Park.
Subsequent scans have since shown that Sturridge will not be fit to feature for the Three Lions in Basel next week, leaving Roy Hodgson with a choice between Danny Welbeck and Rickie Lambert as Wayne Rooney's strike partner.
A Football Association spokesman said: "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 has scored six goals in 15 England appearances since debuting in 2011.