The aircraft belonging to local carrier Agni Air ploughed into the ground just outside Jomsom airport, a gateway to the Annapurna mountain range, shortly after the pilot reported a fault.
"Fifteen people have been killed. Thirteen of them were Indian tourists and the other two were Nepali pilots," police spokesman Binod Singh told AFP.
He said there were six survivors, among them a Nepali air hostess and an Indian man who is being treated for head injuries.
The Danish foreign ministry in Copenhagen said two Danes had also been rescued and were being treated in the city of Pokhara, 60 kilometres (40 miles) from Jomsom.
Basanta Dawadi, of the Pokhara tourism council, said he had spoken to the pair, a man and woman in their early 30s who were both trekkers.
"They told me the plane was about to land and suddenly it ascended and its left wing hit something. The plane rolled and then plunged into the ground. The emergency door opened and they crawled out of the aircraft.
"They told me they lost consciousness and then they were rescued."
The man had foot injuries while the woman had a cut on her throat, Dawadi said.
The Indian Embassy in Kathmandu said two Indian children aged nine and six had been pulled out alive from the wreckage. It released no details about their injuries but said they had been taken to hospital.
The Indian group had chartered the flight from Pokhara for a pilgrimage to Muktinath, a sacred place for Hindus and Buddhists at the foot of the Thorong La pass in the Himalayas, local police spokesman Rajendra Singh Bhandari said.
"A Nepal army barracks is near the accident site which made the rescue of survivors easier," he added, saying they had been airlifted to Pokhara, a city popular with foreign trekkers and tourists.
Dozens of army and police personnel scoured the steep hillside where the plane had come to rest, picking through the wreckage and scattered personal effects.
Bimlesh Lal Karna, head of Nepal's national rescue department, said the pilot had reported a warning light flashing in the cockpit as he descended to Jomsom.
The pilot told air traffic control moments before the crash that he was diverting back to Pokhara, said Karna.
"The aircraft seems to have lost balance," Karna told AFP.
Prime Minister Baburam Bhattarai issued a statement saying he was "deeply saddened" by the accident, while the Indian embassy set up a hotline providing information for desperate relatives.
"I express condolences to the bereaved families and wish for the speedy recovery of the injured," Bhattarai said.
The incident was the second deadly air accident for Agni Air in less than two years.
In August 2010, one of its planes crashed in bad weather near Kathmandu, killing all 14 people on board, including four Americans, a Japanese and a British national.
The latest fatal crash in Nepal -- the fifth in less than two years -- will lead to new scrutiny of the country's numerous small airlines, which provide vital links to remote parts of the country.
Jomsom Airport, at an elevation of 2,707 metres (8,880 feet), has a reputation for being one of the world's most dangerous airfields due to the mountainous terrain on the approach.
However, the US-based Flight Safety Foundation, an independent non-profit organisation researching air accidents across the globe, lists just three fatal crashes at or near the asphalt landing strip since 1970.
In another recent accident in Nepal, a small Buddha Air plane taking tourists on a sightseeing trip around Mount Everest crashed in September last year, killing all 19 people on board.