The body of the girl, identified as Semhar, was found early on Friday evening after police issued a bulletin about her disappearance on the basis of information from her family.
The Tribune de Genève newspaper said it had learned that the girl was strangled.
This has yet to be confirmed by cantonal police.
The force issued a statement saying that investigators believe the case is a “criminal matter” and that the circumstances of the girl’s death were “suspicious”.
The victim is of Ethiopian origin.
She was last seen on Thursday night by a friend who had walked with her from the Drize school in Carouge, Canton of Geneva.
They parted at a crosswalk not far from her home.
One of three children, Semhar lived with her 14-year-old sister, two-year-old brother and mother following the separation of her parents in May, Le Matin reported.
Citing friends of the family, the newspaper said Semhar’s body was found under a bed.
Forensic investigators have begun technical analysis of samples taken from the apartment, police said.
An investigation into the case continues.