Every year around 500,000 people visit Nepal, famed for the world's highest mountain, Everest. It is an especially popular destination for backpackers.
The United States and Britain have issued travel warnings, while Japan and Australia have advised their citizens to stay inside, away from street protests.
Some tour operators from India, which provides almost one-third of Nepal's visitors, were concerned that trade might take some time to return to normal.
Agents in Japan and Singapore, however, said they had not seen much disruption because the crisis had come at the beginning of the rainy season.
Tourism facts
500,000 visitors a year
250,000 local people benefit
Almost 4% of GDP
15% of foreign exchange earnings
Nepalese officials tried to play down the industry's difficulties.
Tourism ministry official Shankar Prasad Koirala said that Nepal was "still the safest destination" for visitors.
But BBC correspondent Jill McGivering says many travellers are having a hard time changing their travel plans because of the disturbances.
Stranded
Several tour companies have cancelled trips, and some tourists already in the kingdom have been stranded because of a curfew and a ban on traffic through the capital.
"Our holiday was destroyed," said Travis Hensley from the American state of Alabama.
"We are just a little nervous but we are not feeling scared as yet," he added. "We are biding our time and hope to get out soon."
Others were more fortunate.
"With everything that's been happening and the fact that things are really tense and fraught on the streets... we're really glad that we're leaving," said Helen, who has been trekking in Nepal for the last three weeks.
Promotion
Nepal launched a three-month tourism promotion campaign in May, directed especially at Indian visitors.
Indian tourist numbers had been dropping since the hijacking of an Indian Airlines plane from Kathmandu in 1999 by Islamist guerrillas.
Also, Maoist rebels have been waging a guerrilla campaign in some areas of Nepal since 1996, and there are fears that current instability could lead to an upsurge in rebel activity.