Sakho picked up the problem in Liverpool's 2-1 Premier League defeat to Crystal Palace on Sunday and will undergo an MRI scan on Monday to determine the extent of the injury.
Coach Didier Deschamps has opted to call up Saint-Etienne defender Loic Perrin as Sakho's replacement.
"Mamadou Sakho has been forced to withdraw from the France squad for the upcoming games against Germany and England after sustaining a sprained knee during Liverpool versus Crystal Palace," a French Football Federation statement read.
"His condition does not allow him to travel to Clairefontaine on Monday as originally planned. The medical staffs of Liverpool and the national team have been contact since Sunday and the player will undergo an MRI scan in England on Monday.
"Didier Deschamps has called up Saint-Etienne's Loic Perrin following Sakho's withdrawal."
France host Germany on Friday, before travelling to England four days later.