The UK-registered Diamond Aircraft went down five kilometres (three miles) south of the international hub, WAM said, citing civil aviation authorities.
"The four-seat plane crashed while on a mission to calibrate terrestrial navigation systems at the airport, with all crew members, three British, and one South African, killed," the news agency said.
An earlier report by the emirate's government media office said the pilot and co-pilot of a small plane had been killed.
The aircraft, owned by US tech giant Honeywell, crashed due to a technical malfunction, it said.
It added that all operations at the airport were running smoothly after "a slight delay and diversion of some flights as a precautionary measure".
Dubai's international airport is one of the world's busiest aviation hubs.
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