The District Public Health Office said that the 309 swine flu cases have been reported over the past three months.
Nearly 380 people underwent tests for the virus and their samples have been sent to the national capital Kathmandu for further tests to determine the stage of their infection, the officials said in a statement.
Running nose, body pain, sore throat, and fever are the symptoms of the disease.
Last month, news reports said the death toll from swine flu in the country reached eight.
It is home to Nepal's first national park, a world heritage property. One of the last populations of single- horned Asiatic rhinoceros lives in the park.