The incident occurred in the city's Hassan II mosque, which was packed during evening prayers Tuesday, the holiest night of the Muslim fasting month of Ramadan, MAP said.
"Eighty-one people, mostly women, suffered light injuries and fractures while some of them fainted," it said.
The panic broke out after a woman raised the alarm over the mouse, sparking a sudden exodus of screaming worshippers.
Among those needing treatment was a pregnant woman who suffered a double fracture in the leg and has been kept under surveillance in hospital.