Police official Hysni Burgaj said a sudden downpour caused the accident.
Authorities still did not know the total number of bus passengers late Saturday.
The bus fell 30 to 40 meters (yards) off a cliff in Dom Gjegjan village, in the district of Puka, police said. The injured were brought to hospitals in the Albanian capital, Tirana, and the northern city of Shkodra.
President Bamir Topi and Prime Minister Sali Berisha visited the injured at the Tirana hospital and promised urgent assistance. The government has declared Sunday a day of national mourning, with flags flying at half-mast.
