Police later confirmed that a body had been recovered.
The attack happened this morning at approximately 10am.
The last fatal crocodile attack in Australia was October last year when a 79-year-old dementia patient was killed after wandering from a nursing home at Port Douglas in Queensland state.
The crocodile was destroyed by local Indigenous rangers and the woman's body was recovered. It is not yet known if her body has been located or if a search is underway.
The Aboriginal ranger was taken by the crocodile about 206km south west of Yirrkala, has not been seen since and police are on their way to the scene, an NT WorkSafe spokesman said.
Officers are still a matter of hours away from the remote location.
NT WorkSafe has started an investigation into the incident.
The corporation have closed their office since they first reported the attack to NT WorkSafe. A CareFlight spokeswoman said the organisation had been stood down from responding as information supplied to them indicated the person was missing.