Local officials contacted by AFP confirmed that Wednesday evening's deluge in the Atlas mountains south of Marrakesh had triggered flash flooding.
The downpour dislodged masses of earth and rocks as high as 20 metres (more than 60 feet) in places that entombed the minibus.
The officials said they could not immediately confirm the death toll.
But 2M said on its website that emergency services recovered 16 bodies after working though the night.
Investment in Morocco's road network has largely focused on the main transport arteries and many rural areas can be reached only by dirt tracks that are vulnerable to extreme weather.
Every year, nearly 3,500 people are killed on the North African country's roads.