A small plane operated by local airline Summit Air went in the wrong direction during take-off and crashed into a parked helicopter, according to the Himalayan Times.
Chief at the Tribhuvan International Airport Raj Kumar Chhetri said the injured persons have been flown on a chopper to Kathmandu for treatment.
The police were tourist cops sent to the area and the dead and wounded are all Nepalese.
A civil administrator, Narendra Kumar Lama, said the four passengers and a flight attendant on the plane were safe.
Assistant Sub-Inspector Rudra Bahadur Shrestha, who was injured in the incident and airlifted to Kathmandu, died at Grande Hospital, hospital sources said.
The aircraft had hit the helicopters of Manang Air and Shree Air.
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The so-called Arabsat 6A satellite was placed into an equatorial orbit some 22,000 miles (36,000km) above the Earth. Arabsat-6A is a Saudi Arabian communications satellite that is created to serve the Middle East, Africa and Europe.
The helicopter was cut in two and three others were damaged.
Tenzing-Hillary airport is often referred to as the world's most unsafe airport because of the short runway and hard approach.
There are about 35 flights and 100 helicopter ferries a day from the airport.
Lukla airport, also known as Tenzing-Hillary airport, is the gateway to Mt Everest.
The airport is named after two men who were first to climb the 8848-metre peak. The pilot of the plane was among three people injured, though the lone stewardess escaped unhurt.
In February a helicopter carrying seven people including the country's tourism minister crashed in bad weather in eastern Nepal, killing seven all on board.