Prime Minister Nawaz Sharif was travelling to the mountainous northern region of Gilgit on a separate aircraft when the accident happened. He returned to Islamabad, his office said.
Norwegian Ambassador Leif Larsen, Philippine Ambassador Domingo Lucenario and the wives of the ambassadors of Malaysia and Indonesia were killed, along with two pilots and a crew member, military spokesman Asim Bajwa said in Twitter posts.
He said initial information indicated the cause was a technical fault. The foreign secretary also said technical problems caused the crash.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"Apparently its engine failed," Foreign Secretary Azaz Chaudhry said. "It was not terrorism."
The Pakistani Taliban claimed they shot down the aircraft but witnesses on the ground, and in other helicopters on the trip, reported nothing to indicate any firing.
Malaysian state media identified the wife of the ambassador as Habibah Mahmud, while Indonesia said its ambassador Burhan Muhammad was injured and his wife, Heri Listyawati Burhan Muhammad, was killed.
Bajwa said the ambassadors of Poland and the Netherlands were among the injured. The ambassadors of South Africa, Lebanon and Romania were also on board, according to a flight list obtained by Reuters. The Romanian Foreign Ministry said its ambassador was alive and uninjured.
An official in Gilgit said nine people had been killed.
"The bodies are so badly torched that they can't be identified," said Sibtain Ahmed, the home secretary of Gilgit-Baltistan.
The Foreign Office said 17 people were on board the Mi-17 when it crashed into a school in Gilgit and caught fire.
Media said there were 11 foreigners and six Pakistanis.
Farmer Shakil Ahmed saw the helicopter crash into the school roof from his house about 100 metres away.
"The helicopter came very close to the helipad, maybe 250 meters in the air, just above the school," Ahmed told Reuters.
"It hovered there for a while and then tried to turn when it crashed. Thankfully there were no kids in the school because it was an off-day for security reasons. The helicopter caught fire and was on fire for over an hour."
Pakistani Taliban militants said they brought down the helicopter with a shoulder-launched missile, adding they had been hoping to shoot down Sharif's aircraft.
"Nawaz Sharif and his allies are our prime targets," Taliban spokesman Muhammad Khurasani said in an emailed statement.
Gilgit, about 250 km (150 miles) north of Islamabad, is not a militant stronghold and the Taliban often claim responsibility for incidents that they had nothing to do with.
The Mi-17 is considered a reliable, no-frills helicopter, first built by Russians for use in hot and high conditions in
Asia, said James Hardy, the Asia-Pacific editor for IHS Jane's Defence Weekly.
"The military has a lot of money and a good reputation for looking after its equipment," he said. "The air force is well trained and highly professional."
The Pakistan military was believed to operate about 29 Mi-17s and the air force about six, he said. Media have reported four other Mi-17 crashes in Pakistan in the last 11 years.
