The vehicular accident occurred Saturday in Dassu Tehsil in the Gilgit area of Kohistan district, Dawn reported Monday.
CNN put the death toll at 27, including 25 soldiers.
Dawn quoted local police that an army colonel was among those killed.
Sources told Dawn the driver of the privately owned bus lost control of the vehicle at a sharp turn on the Karakoram Highway, sending it plunging into the river.
The report said the military confirmed the deaths of 23 army personnel along with that of the driver and a bus conductor. The soldiers were with a light infantry battalion and were proceeding on leave.
It was not clear how many people in all were in the bus or how many were injured. Dawn said rescue personnel had retrieved the bodies of the dead from the river.