The Twin Otter aircraft, operated by Tara Air was travelling from Pokhara to Jomsom and lost contact with the control tower shortly after taking off.
Two of the passengers are thought to be foreigners. Officials said two children were also on board.
Nepal’s aviation industry has a poor safety record.
But Sanjiv Gautam, director general of Nepal’s Civil Aviation Authority, told the BBC’s Nepali Service this was a new aircraft and weather was good. “We are surprised to know that it has gone missing,” he said.
A helicopter search is being hampered by poor weather conditions.
Pokhara is a resort town some 200 kilometres (125 miles) west of the capital Kathmandu. Jomsom, a short distance further north, is the starting point for many people trekking in the Himalayas.
There are no landing strips between the two locations and the plane took off at around 7:55am local time (2:10 GMT).
Since 1949 – the year the first aircraft landed in Nepal – there have been more than 70 different crashes involving planes and helicopters, in which more than 700 people have been killed. In 2013, the European Union banned all Nepalese airlines from flying there.