The virus, borne by mosquitos which breed in stagnant water, has killed 17 people in Khyber Pakhtunkhwa province since August 19, 14 of them in Swat.
Doctors said the number of patients is increasing every day.
Dengue causes high fever and severe joint and muscle pains.
"So far 14 people have died due to this disease while 4,934 persons tested positive. We have declared a health emergency in the district," Abdul Khaliq, district health officer in Swat, told AFP by telephone.
Khaliq said the outbreak has been declared an epidemic.
"It is becoming dangerous. Dengue larvae are everywhere, in and outside houses, in streets and all other places," he said.
Officials said they believed infected mosquito larvae had been brought from the eastern city of Lahore in water in a consignment of old tyres.
An outbreak in Lahore, Pakistan's second largest city, in September 2011 killed 362 people and infected more than 21,000.
Doctor Qutbuddin Kakar, focal person for the World Health Organization (WHO) on dengue, confirmed to AFP the virus has claimed 14 lives in Swat and said it had been declared an epidemic.
"WHO is coordinating with the local authorities, we are helping them to control the disease and also providing them technical support," Kakar said.
The WHO was also helping in fumigation, identifying which strain of dengue is involved and which localities need most attention.
Hospitals in Mingora, the main town in Swat, are struggling to cope with the influx of patients, who complained of a lack of facilities and basic medicines.
"We have not enough beds, no medicines and sometimes we go outside to have blood tests in private laboratories," Hamid Khan, a relative of one patient, told AFP.
"My brother had fever and we are worried because the blood test was positive."
There is no specific treatment for dengue but proper medical care for severe cases greatly reduces the risk of death, according to the WHO.
Officials in Mingora's main Saidu Sharif hospital said a special 100-bed ward has been set up to deal with dengue cases.
Shafiullah Khan, a senior health official, told AFP that a number of preventative measures including fumigation have been taken to control the outbreak.
"We have already launched a fumigation drive. Fumigation machines are spraying all over the Swat valley," Khan said.
"Health workers are also mobilising residents and a door-to-door awareness campaign is also on," he said.
People have been advised to use mosquito nets and insect repellents and to avoid storing water in open pots where the larvae can breed.
Khan said dengue was spreading to other districts in the northwest.
"So far 300 cases of dengue-positive patients have been reported in nine other districts," he said, adding that three people died of the disease in the nine districts.