The setback occurred during the Black Stars training exercise in the United Arab Emirates.
One of five players summoned to the camp from the beginning, it is unclear if the 22-year-old could recover in time for the June 21-July 19 continental championship in Egypt.
"Switzerland based Ghanaian defender Nuhu Musah has been granted permission to travel back to Switzerland at the request of his club St. Gallen," the Ghana Football Association Normalisation Committee announced via their official website on Thursday morning.
"Musah sustained an injury during Black Stars training on Wednesday.
"After an initial medical examination by the Black Stars medical team, Nuhu has been permitted to return to his club for further assessment. Nuhu, will be accompanied by Team Psychologist, Dr Patrick Ofori.
"The GFA Normalization Committee wishes Nuhu a speedy recovery."
Nuhu's injury is the latest setback for Ghana ahead of the Afcon having lost Crystal Palace's Jeffrey Schlupp, Leicester City defender Daniel Amartey, Sassuolo midfielder Alfred Duncan, Nicholas Opoku of Udinese and Harrison Afful of Columbus Crew.
The Black Stars have been pitted against defending champions Cameroon, Benin and Guinea-Bissau in Group F of the Afcon. They will be facing Namibia in a preparatory fixture on Sunday.