Hudson-Odoi suffered a shoulder injury during training over the weekend, days before both Tammy Abraham and Thiago Silva returned to training at the club’s Cobham base.
The extent of Smith Rowe’s fitness concerns are unknown but are likely severe enough to rule him out of Wednesday’s crucial Euros group game.
Aidy Boothroyd said on Tuesday: "Callum is definitely out and he has gone back to his club, Emile Smith-Rowe is also very doubtful."
The Young Lions are on the brink of an early exit after losing their opening two games to Switzerland and Portugal.
Boothroyd's side can still reach the summer's knockout stages if they beat Croatia by two goals on Wednesday and Switzerland lose to Portugal.
England have failed to have a shot on target from open play in Slovenia and, after breezing through qualifying unbeaten, have been poor at the tournament.