The Agni Air plane plunged into a hill close to Jomsom near the Annapurna mountain range, police spokesman Binod Singh told.
"The plane was about to land at Jomsom airport. It hit a muddy slope and the plane is now buried in the side of the hill," he said.
"Fifteen people have been killed. Thirteen of them were Indian tourists and the other two were Nepali pilots.
"There are six survivors, among them one Nepali air hostess," he added.
The passengers had chartered the flight to take them from the central tourist hub of Pokhara to Muktinath, a sacred place for Hindus and Buddhists at the foot of the Thorong La Himalayan mountain pass, said Rajendra Singh Bhandari, Nepal police regional spokesman.
"A Nepal army barracks was near the accident site which made the rescue of survivors easier," he added.
Agni Air marketing manager Pramod Pandey said two Danish nationals were among the passengers, although their condition was not known.
The crash was the second deadly air accident for Agni Air in less than two years.
In August 2010 one of the private carrier's Everest-bound planes crashed in bad weather near Kathmandu, killing all 14 people on board, including four Americans, a Japanese and a British national.
The craft had been returning to Kathmandu after poor visibility prevented it from landing at Lukla, its intended destination in a popular trekking spot in eastern Nepal.
Air travel is popular in Nepal, which has only a very limited road network. Many communities, particularly in the mountains and hills, are accessible only on foot or by air.
Aviation accidents are relatively common, particularly during the summer monsoon, when visibility is usually at its worst.
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.
The Beechcraft plane, carrying 10 Indians, two Americans, one Japanese citizen and three local passengers, came down in heavy rain and fog at Godavari, about 10 kilometres (six miles) from Kathmandu.
The three Nepalese crew also died in the accident as the plane smashed into wooded slopes.
An investigation blamed that crash on a combination of poor visibility and human error.
Ten months earlier a Twin Otter plane carrying three crew and 19 passengers, including one American, smashed into a mountainside shortly after taking off from a small airstrip 140 kilometres east of Kathmandu.
The passengers were mostly Bhutanese citizens on a religious tour of Nepal and had chartered the Tara Air plane to take them to a Buddhist holy site in the area.