The driver lost control of the vehicle on a bend near the city of Chilas, in the Gilgit-Baltistan region, around dawn, falling into a rocky ravine where the River Indus flows.
"The local Ulema (Muslim leader) announced the news of the accident from the loudspeaker of the mosque and urged the people to donate blood for the injured," Azmat Shah, a police official in the city told AFP.
"Rescue operations have been completed. Among the 21 injured, the condition of five is very critical."
The bus was travelling from the capital Islamabad to Gilgit.
Road accidents with high fatalities are common in Pakistan, where safety measures are lax, driver training is poor and transport infrastructure often decrepit.
