The young midfielder suffered a dead leg in Thursday’s 9-1 win over Serbia and will not travel to play Ukraine in Slovakia on Monday.
Palmer skippered Lee Carsley’s side to a comprehensive victory in Nottingham, but was forced off after 52 minutes.
“I think Cole would be fine, but we don’t take any chances with any of the players,” said Carsley.
“If there is a slight doubt that they’re going to miss a game at the weekend, we get them back to the clubs as quickly as we can.
“We could’ve kept Cole here another day and see how it was, but we didn’t think it was right. Everyone else is fine, a few colds and sniffles.”
Chelsea will therefore hope Palmer is fit to play in the weekend clash with Arsenal, for which they also hope to have Reece James, Axel Disasi, Nicolas Jackson and Benoit Badiashile available after injuries.
It also means Liverpool’s Harvey Elliott, who scored twice in the City Ground rout, will captain the Young Lions in Kosice.
Defending champions England, after their Euro 2023 victory in Georgia in the summer, are top of Group F following their opening two wins.