The French Football Federation has announced the Barcelona winger will leave the squad ahead of the world champions' final Group F game against Portugal in Budapest on Wednesday.
Dembele suffered the injury after being introduced as a second-half substitute in Saturday's 1-1 draw with Hungary. He played only 30 minutes before being withdrawn late on.
It has now been determined the 24-year-old will not be fit to play any further part in the tournament following scans in a Budapest hospital on Sunday.
A statement from the FFF read: "The recovery times are incompatible with his retention in the group currently playing UEFA Euro 2020."