No group immediately claimed responsibility for the attack and the motive for the shooting was unclear.
Muhammad Ali Johar, a spokesman for the regional government, said the attackers opened fire on the bus on Saturday evening and the wounded were taken to a local hospital.
Ghulam Abbas, a spokesperson for the Gilgit-Baltistan Police, told the dpa news agency that two soldiers were among those killed.
According to Abbas, another 26 passengers were wounded in the attack – some with bullet injuries.
The bus was travelling the Karakoram Highway, one of the highest roads in the world.
The attack, according to officials, took place at about 6:30pm (13:30 GMT) when the attackers opened fire at the bus and it subsequently collided with an oncoming lorry.
No group immediately claimed responsibility for the attack and the motive for the shooting was unclear.
“The government will ensure that the terrorists involved in the attack are given the appropriate punishment,” the chief minister of Gilgit-Baltistan, Haji Gulbar Khan, said in a statement.
Chilas lies in the mountainous region of Gilgit Baltistan, near the northwestern province of Khyber Pakhtunkhwa, where attacks have been rising in recent years, including some claimed by the Pakistani Taliban, or Tehreek-e-Taliban Pakistan (TTP).
Chilas is a popular stopping point for tourists and is also near a China-backed dam under construction.
The attack came amid an uptick in armed attacks across the country, particularly in Khyber Pakhtunkhwa and southwestern Balochistan. Both provinces border Afghanistan.
In July, a suicide bomber detonated explosives at a political rally in northwestern Pakistan’s Bajaur district, killing at least 44 people and wounding nearly 200, according to officials.
Last month, a Pakistan Air Force base came under attack in central Punjab province, which the military said was repulsed successfully.