The Northern Territory Health Department says the Territory's first case of dengue fever in 70 years is a complete mystery.

The department says the mosquito that carries dengue fever does not exist in the Territory.

It is therefore at a loss to explain how a man who did not travel outside of the Territory contracted the virus.

Dr Vicki Krause from the Centre for Disease Control says her only explanation is a dengue mosquito may have come into the Territory by ship or cargo.

"At this time we do not think that this is a risk to the public; that it does appear to be a one-off case," she said.

"Extensive mosquito trapping has occurred and we have not found any mosquitoes that are capable of spreading the dengue virus so it does appear to be a sporadic case."

Meanwhile, biting midge activity will peak tomorrow on the full moon.

The Health Department says Top End residents should avoid coastal mangrove areas.