It is still hoped Sturridge will be fit enough to be involved in Tuesday's encounter with Ukraine in Kiev.
"Daniel Sturridge has returned to Liverpool for further treatment," it was reported on the FA website.
"The Liverpool forward will return to his club with the intention of joining the England squad again at the weekend and travelling to Ukraine."
The news is not unexpected given Sturridge admitted at the weekend he was worried about shooting due to the discomfort he was experiencing.
Hodgson confirmed that with Sturridge's withdrawal, Lambert will lead the line for the qualifier.
Referring to Caulker, Hodgson added: "Unfortunately, in training he turned his ankle. It's not a serious matter but it will keep him out of the game.
"It won't keep him out of the Ukraine game, he's expected to do some running, but he won't be on the bench."
England team: Hart, Walker, Jagielka, Cahill, Cole, Gerrard, Lampard, Wilshere, Lambert, Walcott, Welbeck.