The bus was enroute from the city of Zagora when it plunged down a 492-foot ravine, the Indo-Asian News Service reported.
Thirty-seven people were killed instantly while five others died in a hospital later.
Police said most of the injured were taken to a hospital in Marrakesh.
Morocco's roads are rated to be among the deadliest in all of Africa.
Figures provided by the country's transport ministry indicate last year alone 4,200 people were killed in road accidents, an increase of 12 percent over the previous year.