Cherry suffered a concussion after "an accident in the team hotel earlier this week" and is now following the current return-to-play protocols, the federation said.
That means he will be unavailable for at least the next 12 days.
"The decision was therefore taken to end his tournament involvement on medical grounds after he injured his head on Monday, slipping on hotel stairs, on a team day off," it said.
Cherry added: "I'm hugely disappointed to be leaving the squad with concussion.
"I've loved my time in camp over the summer and gaining my first World Cup cap on Sunday against South Africa.
"I want to wish the team all the best for the remainder of the competition."
Edinburgh hooker Stuart McInally, who was initially put on standby following a concussion sustained by Ewan Ashman last week, has been called up to replace Cherry.
Ashman is continuing his return-to-play protocols and is currently on track to be available for selection next week.
Scotland kicked off their World Cup campaign with an 18-3 defeat by defending champions South Africa.
Next up for them in Pool B is Tonga in Nice on September 24th, followed by Romania in Lille six days later before they face Ireland in Paris on October 7th.
