The drownings occurred in the Kunhar River that flows through Khyber Pakhtunkhwa province, at a hilly tourist spot in Beesian village, some 200 kilometres (120 miles) north of Islamabad.
The deep, rocky and fastflowing river is popular for white-water rafting.
“The girl, Safia Atif, was trying to take a selfie along the river when she slipped and fell,” local police official Arshad Khan told AFP, explaining the incident was witnessed by other tourists.
Safia’s mother Shazia Atif then jumped in to save her daughter but was swept away.
“Seeing both his wife and daughter drowning, the father Atif Hussain also jumped in to rescue them but he met a similar fate,” Khan added.
“The dead bodies of the mother and daughter have been recovered while we are still looking for the body of Hussain,” he added.
He said the parents were doctors from Punjab province and had taken their family to the area on holiday. They are survived by a nine-year-old daughter and six-year-old son who witnessed the event.
“Both of them are in the protective custody of the local administration and they will be handed over to their family members when they arrive,” he said.
The incident was confirmed by other administration officials and family members of the deceased.
One official said the government had put up signs warning people not to go near the river.
“Each year around a dozen people drown here,” he said requesting not to be named.
“This is a tourist spot and people usually come here for picnic and most of them are outsiders who have no idea about the depth of the river,” he said.
So-called “selfie deaths” have surged with the global rise of smartphones.
On July 5, Peruvian police recovered the body of a South Korean tourist under a waterfall in the Amazon jungle, days after he fell in while taking a photo of himself.
A week earlier, a 51-year-old German tourist plunged 200 metres (650 feet) to his death while posing for a photo on a mountainside at Peru’s top archaeological site, Machu Picchu.